Carnegie Learning Algebra I Student Text Volume 1 3rd Edition Chapter 3 Linear Functions
Page 174 Problem 1 Answer
Given Marshall High School, Athletic Association sells tickets for the weekly football games.
Students pay $5 and adults pay $10 for a ticket.
we have to find how much money would the athletic association collect if 100 students and 50 adults buy tickets to the game.
Find individual prices of student’s and adult’s pay for tickets and sum them.
Given students pay $5 and adults pay $10 for a ticket.
The money collected by 100 students As
=100×5=$500
The money collected by 50 adult Aa
=10×50=$500
The total amount of money= money collected by students+ The money collected by adult
=500+500
=$1000
Hence, Marshall High School, Athletic Association collected $1000.
Marshall High School, Athletic Association collected $1000 by selling tickets.
Page 174 Problem 2 Answer
Given Marshall High School, Athletic Association sells tickets for the weekly football games.
Students pay $5 and adults pay $10 for a ticket.
we have to find how much money would the athletic association collect if 125 students and 75 adults buy tickets to the game.
Find individual prices of student’s and adult’s pay for tickets and sum them.
Given students pay $5 and adults pay $10 for a ticket.
The money collected by 125 students As
=125×5=625
The money collected by 75 adult Aa
=75×10=750
The total amount of money= money collected by students+ The money collected by adult
=625+750
=$1375
Hence, Marshall High School, Athletic Association collected $1375.
Marshall High School, Athletic Association collected $1375 by selling tickets.
Page 174 Problem 3 Answer
Given Marshall High School, Athletic Association sells tickets for the weekly football games.
Students pay $5 and adults pay $10 for a ticket.
we have to find how much money would the athletic association collect if 97 students and 116 adults buy tickets to the game.
Find individual amount of student’s and adult’s pay for tickets and sum them.
Given students pay $5 and adults pay $10 for a ticket.
The money collected by 97 students As
=97×5 =475
The money collected by 116 adult Aa
=116×10=$1160
The total amount of money= money collected by students+ The money collected by an adult
=475+1160
=$1645
Hence, Marshall High School, Athletic Association collected$1645.
Marshall High School, Athletic Association collected $1645 by selling tickets.
Page 174 Problem 4 Answer
Given Marshall High School, Athletic Association sells tickets for the weekly football games.
Students pay $5 and adults pay $10 for a ticket.
Here we have to explain how you can determine the total amount of money collected if you know the number of student tickets sold and the number of adult tickets sold.
To determine the total amount of money collected First find individual prices of student’s and adult’s pay for tickets
For example, let the ticket price is y and we sell x ticket then, the total money we get is xy.
The total amount of money collected is sum of amount of student’s and adult’s pay for tickets
We can determine the total amount of money collected find individual prices of student’s and adult’s pay for tickets and sum of amount of student’s and adult’s pay for tickets.
Page 174 Problem 5 Answer
Given Marshall High School, Athletic Association sells tickets for the weekly football games. Students pay $5 and adults pay $10 for a ticket
Here we have to explain how your expression represents this problem situation.
The expression previews question is5s+10a
here 5 represent the cost of a student Ticket and s represent number of student ticket sold, 10 represents the cost of a adult Ticket, and a represent number of student tickets sold, So5s+10a
represent total amount collected.
Here 5s represent the amount collected from student tickets and 10a represent the amount collected from adult tickets.
Page 176 Problem 6 Answer
Here we have to tell if we know the number of student tickets sold, can we determine the total amount of money collected.
No, we can’t determine the total amount of money collected because the total amount is a dependent function we also have to know the number of adult tickets sold to determine the total amount of money collected
No, we can’t determine the total amount of money collected because the total amount is a dependent function we also have to know the number of adult tickets sold.
Page 176 Problem 7 Answer
Here we have to tell if you know the total amount of money collected, can you determine the number of student and adult tickets sold.
No, we can’t determine the number of student and adult tickets sold.
Because the number of student or adult tickets is a dependent function we also have to know at least the number of student or adult tickets.
No, we can’t determine the number of student and adult tickets sold because the number of student or adult tickets is a dependent function we also have to know at least the number of student or adult tickets.
Page 176 Problem 8 Answer
Given the football team is playing in an out-of-town tournament.
The athletic association needs to raise $ 3000 to send the team to this tournament.
The money raised from selling tickets to a special event home game will be used toward the tournament cost.
We have to use your equation to complete the given table.Use equation 5s+10a=3000.
The first segment has a statement of s so its amount name is Number of Student Tickets and its units are tickets.
The subsequent segment has the articulation a so its amount name is Number of Adult Tickets and its units are tickets. Since every understudy ticket is $5, the articulation 5s in the third section has an amount name of Money Collected From Student Tickets and has units of dollars.
Since every grown-up ticket has an expense of $10, the articulation10a in the fourth section has an amount name of Money Collected From Adult Tickets and units of dollars.
The articulation 5s+10a in the fifth section then, at that point, has an amount name of Total Amount Collected and has units of dollars.
Since the situation is 5s+10a=3000, the aggregate sum gathered is consistently $3000 so the four cells in the lower part of the fifth section are then each of the 3000:
Now fill the value of value of money Collected From adult Tickets and student Tickets by multiplying 5 by number of Student tickets and 10 by number of adult tickets
Fill in the sums for the cash gathered from understudy tickets by deducting the cash gathered from grown-up tickets from 3000. Fill in the sums for the cash gathered from grown-up tickets by deducting the cash gathered from understudies tickets from 3000
Now fill the remaining column by using equation
The table is
Page 177 Problem 9 Answer
Given Carla and Robena sell game tickets. They have already sold 95 student tickets.
Carla says that they need to sell 252 adult tickets to reach the goal of $ 3000.
Robena says that they need to sell 253 adult tickets to reach the goal.
Here we have to tell who is correct and explain our reasoningPut the values of adult tickets in the problem function.
We know the function of this problem is 3000=5s+10a
We already sold 95 student tickets then 3000=5×95+10a
3000=475+10a
2525=10a
a=252.5
Means Robena is right they need to sell 253 adult tickets to reach the goal because we didn’t sufficient amount of money by sell 252 adult tickets.
Robena is right they need to sell 253 adult tickets to reach the goal because we didn’t sufficient amount of money by sell 252 adult tickets.
Page 178 Problem 10 Answer
Given the x-axis represent the number of student tickets sold.
Let the y -axis represent the number of adult tickets sold.
Determine the x-intercept and the y-intercept for the transformed equation here we have to explain what each intercept means in terms of the problem situation and what do we notice.
Find the points where the function graph meets the x and y-axis.
Leta=y ands=x then, y=−1/2x+300
For x-intercept At x-axisx=0 then graph intercept x-axis at point(600,0)
For y-intercept At y-axisy=0 then graph intercept y-axis at point(0,300)
Hence, equation intercept x-axis at (600,0) and y-axis at(0,300).
And the graph is
The transformed equation intercept x-axis at (300,0) and y-axis at(0,600) and the graph is
Page 179 Problem 11 Answer
Given the equationa=−1/2s+300
We have to use the x-intercept and y-intercept to graph the equation.
Plot the points of x-intercept and y-intercept now draw a straight continuous line that crossing through intercept points.
From the previews part the transformed equation intercept x-axis at(600,0) and y-axis at(0,300).
now plot the points and draw a straight continuous line that crossing through these points.
Graph of the equation by using x-intercept and y-intercept is
Page 179 Problem 12 Answer
Given the equationa=−1/2s+300
We have to find the athletic association sold 400 student tickets.
Determine how many adult tickets they must sell to reach the $3000 goal.
Substitute the value of student tickets in the equation
The athletic association sold 400 student tickets thena=−1/2s+300
substitutes=400
a=−1/2×400+300
=−200+300
=100
Hence, the athletic association sells 100 adult tickets to reach the $3000 goal.
The athletic association sells 100 adult tickets to reach the $3000 goal.
Page 179 Problem 13 Answer
Given the equation a=−1/2s+300
We have to explanation if the athletic association sold 400 student tickets and 200 adult tickets then an you use the graph to determine how much money is collected.
No. The graph just gives the various mixes of grown-up and understudy tickets offered to gather an aggregate sum of $3000.
The diagram goes through the point (400,100) not (400,200) so it can’t be utilized to discover the measure of cash gathered.
No, can’t use the graph to determine much money is collected.
Page 180 Problem 14 Answer
Given let’s consider reaching the $ 3000 goal for ticket sales by analyzing the number of adult tickets sold.
If the association knows that 150 adult tickets have been sold, how many student tickets would they need to sell to reach their goal.
We have to find transform the equation 5 s+10 a=3000 to solve for the number of student tickets.
Do Adding, Substracting, multiplication, and division to transform the equation
Given equation is 5s+10a=3000
We have to find transform this equation to solve for the number of student tickets.
Add−10a on both sides 5s=3000−10a
Divide 5 by both sides s=600−2a
Hence, the transform the equation to solve for the number of student tickets iss=600−2a.
The transform the equation to solve for the number of student tickets iss=600−2a.
Page 180 Problem 15 Answer
Given let’s consider reaching the $ 3000 goal for ticket sales by analyzing the number of adult tickets sold.
If the association knows that 150 adult tickets have been sold, how many student tickets would they need to sell to reach their goal.
We have to find how many student tickets must the athletic association sell on homecoming weekend to reach their goal of $3000.
Use the transform the equation to solve for the number of student tickets.
The transform equation to solve for the number of student tickets iss=600−2a.
Association knows that 150 adult tickets have been sold substitute a=150
s=600−2×150
s=600−300
s=300
Hence, the athletic association sells 300 student tickets to reach the $3000 goal.
The athletic association sells 300 student tickets to reach the $3000 goal.
Page 180 Problem 16 Answer
Given let’s consider reaching the $ 3000 goal for ticket sales by analyzing the number of adult tickets sold. If the association knows that 150 adult tickets have been sold, how many student tickets would they need to sell to reach their goal.
We have to determine the x-intercept and the y-intercept of the graph described by this equation.
Explain what the intercepts mean in terms of the problem situation.
Find the points where the function graph meets the x and y-axis.
The transform equation to solve for the number of student tickets iss=600−2a
Leta=x and s=y then y=600−2x
At x-axisy=0 then graph intercept x-axix at point(300,0)
For y-intercept At y-axisx=0 then graph intercept y-axis at point(0,600)
An intercept of any function is a point where the graph of the function crosses, or intercepts, the x-axis or y-axis
The transformed equation intercept x-axis at (300,0) and y-axis at(0,600) and an intercept of any function is a point where the graph of the function crosses, or intercepts, the x-axis or y-axis.
Page 181 Problem 17 Answer
Given the equations=600−2a
we have to identify the slope of the graph. Interpret its meaning in terms of the problem situation use the formula of the slope of the graph
From the previews part, we know that the graph crossing through(300,0)
and(0,600) points. then the slope of the graph ism=600−0/0−300
=−600/300
=−2
Hence, the slope of graph is−2.
The slope of the graph is−2.
Page 181 Problem 18 Answer
Given the equation which represents the tickets problem for the athletic association.
a=−1/2s+300
We have to compare the x-intercepts and the y-intercepts of the two graphs we just created and what do we notice
The x – and y-capture for the first graph was (600,0), and (0,300) and addressed selling 600 student tickets and 0 grown-up passes to come to the $3000 objective and selling 0 student tickets and 300 grown-up passes to come to the$3000 objective.
The x-and y-blocks for the subsequent graph were (300,0) and (0,600) and addressed selling 300 grown-up tickets and 0 student passes to come to the$3000 objective and selling 0 grown-up tickets and 600 student passes to come to the the$3000 objective.
The intercept are then exchanged in the two graphs and have similar portrayals with regard to the issue.
By comparing the x-intercepts and the y-intercepts of the two graphs we notice that the intercept are then exchanged in the two graphs and have the same representations in the context of the problem.
Page 181 Problem 19 Answer
Given students that want to attend the special event game must purchase their tickets at school prior to the game.
So far, 189 students bought tickets for the game.
The athletic association wants to know how many adult tickets they must sell in order to reach their goal of $3000.
However, they want a method to make forecasting how many adult tickets they must sell more efficient.
Another way to determine the number of adult tickets that must be sold to reach a goal of $3000 is to transform the equation to isolate a first.
a=−1/2s+300
Now, substitute the information you know into the transformed equation.
We have to answer is there a way to determine the total amount of money collected from either graph and explain why or why not.
Yes. Both graphs represented the different combinations of adult and student tickets sold to collect a total of $3000.
If you didn’t know the amount collected that they represented, you could still find it by using one of the intercepts.
If we used the y-intercept(300,0) for the second graph, you would know the total amount collected is 10(300)=$3000 since the x-coordinate represents the number of adult tickets sold and each student ticket was sold for $10.
Yes. Both graphs represented the different combinations of adult and student tickets sold to collect a total of$3000.
Page 181 Problem 20 Answer
Given 5s+10a=3000
we have to identify the units of measure for 5 of the given equation.Simplify the term 5s to identify the units of measure of 5.
We know this equation represents the athletic association needs to raise $ 3000 and students pay $5 and adults to pay $10 for a ticket.
So 5s total amount by selling student ticket and we knows is the count of student ticket.
Let unit of measurement of 5 is x.
then, x×student ticket=dollars
x=dollars student ticket
Hence, here 5 represents the cost of the student ticket in the given equation.
Here 5 represents the cost of the student ticket
Page 181 Problem 21 Answer
Given 5s+10a=3000
we have to identify the units of measure for s of the given equation.
Here s represents the number of the student ticket sold in the given equation.
Here s represents the number of the student ticket sold.
Page 181 Problem 22 Answer
Given 5s+10a=3000
we have to identify the units of measure for 10 of the given equation.
Simplify the term10a to identify the units of measure of 10.
We know this equation represents the athletic association needs to raise $ 3000 and students pay $5 and adults to pay $10 for a ticket.
So 10a total amount by selling adult tickets.
Let unit of measurement of 10 is x. then, x×adult ticket=dollars
x=dollars adult ticket
Hence, here 10 represents the cost of the adult ticket in the given equation.
Here 10 represents the cost of the adult ticket.
Page 174 Problem 23 Answer
Given 5s+10a=3000
we have to identify the units of measure for an of the given equation.
Simplify the term10a to identify the units of measure of a.
We know this equation represents the athletic association needs to raise $ 3000 and students pay $5 and adults to pay $10 for a ticket.
So 10a total amount by selling adult ticket and we know 10 is the rate of per adult ticket.
Let unit of measurement of a is x. then, dollars adult ticket.x=dollars
x=dollars.adult ticket/dollars
x=adult ticket
Hence, here a represents the number of adult tickets sold in the given equation.
Here a represents the number of adult tickets sold.
Page 181 Problem 24 Answer
Given 5s+10a=3000
we have to identify the units of measure for 3000 of the given equation.
Simplify the term 5s+10a to identify the units of measure of 3000.
We know this equation represents the athletic association needs to raise $ 3000 and students pay $5 and adults to pay $10 for a ticket.
So, 3000 total amount by selling both tickets and we know 5 is the rate of per student ticket,s is the count of student ticket,10 is the rate of per adult ticket and a is the count of adult ticket.
Let unit of measurement of 3000 is x.
then, x=dollars/ student ticket.student ticket+dollars/adult ticket.adult ticket
x=dollars+dollars
x=dollars
Hence, here3000 represents the total amount collected in the given equation.
Here3000 represents the total amount collected
Page 182 Problem 25 Answer
Given analyzed the units of each part of the equation5s+10a=3000
we have to write the next sentence in the worked example after dividing out the two different units of measure and what does this tell you about the original equation So in the first product student tickets were canceled and in the second product, adult tickets were canceled.
dollars+dollars=dollars
This tells me the original in terms of dollars.
The next sentence in the worked example after dividing out the two different units of measure
dollars+dollars=dollars
This tells me the original in terms of dollars.
Page 184 Problem 26 Answer
Given the equation5s+10a=3000
we have to explain what happened to the units of students and dollars when converting from standard form to slope-intercept form in the worked example.
If we convert this equation in standard form to slope-intercept the units of students and dollars were canceled.
And the equation in terms of an adult tickets.
In standard form to slope-intercept, the units of students and dollars were canceled and the equation in terms of adult tickets.
Page 184 Problem 27 Answer
Given the equation5s+10a=3000
we have to convert the standard form of the original given equation to slope intercept form to represent the number of student tickets.
Show and explain the final units for the equation.
Analyze the units of each part of the equation.
From question 7, slope intercept form of 5s+10a=3000 is s=−2a+600
From question 9, the unit of slop -2 is student tickets
adult tickets then the units for the equation
s = −2 a + 600
student tickets=student tickets/adult tickets
adult tickets+student tickets
student tickets= student tickets=+student tickets
The final unit for the equation is student tickets.
The final unit for the equations=−2a+600 is student tickets.
Page 185 Problem 28 Answer
Given Katie received a $ 75 gift card for her birthday. She decides to buy new music and movies for her electronic notebook with a gift card.
Songs cost $1.29 each and movies cost $14.99 each.
we have to write an equation to represent this problem situation.
Use s to represent the number of songs and m to represent the number of movies.
The cost of each song is $1.29 and if she buyss songs then she spends1.29s dollars and the cost of each movie is $14.99 and if she buy sm movie then she spends14.99m
Dollars She has $75 gift card for her birthday and she will spend 1.29s+14.99m
An equation to represent this problem situation is1.29s+14.99m=75
An equation to represent this problem situation is 1.29s+14.99m=75.
Page 185 Problem 29 Answer
Given Katie received a $ 75 gift card for her birthday.
She decides to buy new music and movies for her electronic notebook with the gift card.
Songs cost $1.29 each and movies cost $14.99 each and
We have to complete the table to show what each expression represents in this problem situation.Heres represents number of songs she purchased so 1.29 represents cost of each song then1.29s represents total amount she spends on songs.
And m represents number of movies she purchased so 14.99 represents cost of each movie then 14.99m represents total amount she spends on movies.
The expression 1.29s+14.99m represents the total amount she spends and 75 represents the amound she can spends.The table to show what eachexpression represents in this problem situation is
The table to show what each expression represents in this problem situation is
Page 185 Problem 30 Answer
Given Katie received a $ 75 gift card for her birthday. She decides to buy new music and movies for her electronic notebook with the gift card. Songs cost $1.29 each and movies cost $14.99 each.
we have to find if Katie buys 20 songs, what is the greatest number of movies she can buy
Find the remaining amount she has after buying 20 songs then how many movies she buy in remaining amount.
Each song cost is $1.29 the 20 song cont is 1.29×20=25.8
Now remaining amount she has $75−$25.8=$49.2
If each movie cost is $14.99 then she buy 49.2/14.99≈3.27
So she can buy maximum 3 movies
If Katie buys 20 songs then now she can buy maximum 3 movies.
Page 186 Problem 31 Answer
Given Katie received a $ 75 gift card for her birthday. She decides to buy new music and movies for her electronic notebook with a gift card.
Songs cost $1.29 each and movies cost $14.99 each.
We have to find if Katie buys no movies, what is the greatest number of songs she can buy?
What does this number represent Find the remaining amount she has after buying no movies then how many songs she buy in remaining amount.
She buys no movies then she can spend all of the $75 on songs
If each song cost is $1.29 then she buys75/1.29≈58.1
So she can buy maximum 58 songs.
If Katie buys no movies then she can buy maximum 58 songs
Page 186 Problem 32 Answer
Given Katie received a $ 75 gift card for her birthday. She decides to buy new music and movies for her electronic notebook with the gift card.
Songs cost $1.29 each and movies cost $14.99 each.
we have to find if Katie buys no songs, what is the greatest number of movies she can buy and what does this number represent
Find the remaining amount she has after buying no songs then how many movies she buy in remaining amount.
She buys no songs then she can spend all of the $75 on movies
If each movie cost is $14.99 then she buys 75/14.99≈5
So she can buy maximum 5 movies.
If Katie buys no songs then she can buy maximum 5 movies.