Envision Math Grade 8 Volume 1 Chapter 2 Analyze And Solve Linear Equations
Page 117 Exercise 1 Answer
Given
Meili going to pick the apple and between the apples.
Which orchard should mei li choose?
We simply going to solve each of given equation and find value for each.
20x =7.25
Divide both side of the equation by 20.
x ≈ 0.36
Price per lb for annie’s apple orchard is about $0.36
12x = 5
Divide both sides of the equation by 12
x ≈ 0.42
Now we can see that price per lb for franklin’s fruit orchard is about x ≈ 0.42
We simply compare values for first and second apple orchard to see which is cheaper.
0.36 < 0.42
Annie’s apple orchard is cheaper than franklin’s fruit orchard and that is why mei li should choose annie’s apple orchard.
She should pick annie’s apple orchard.
Page 117 Exercise 1 Answer
We need to explain what information provided can be used to support the answer.
In Annie’s Apple Orchard, 20 lb costs $7.25
In Franklin’s fruit Orchard, 12 lb costs $5.00
The unit rate of each will be,
For Annie’s,
\(\frac{7.25}{20}=0.3625\)For Franklin’s,
\(\frac{5}{12}=0.417\)Thus, Meili choose Franklin’s fruit Orchard since it costs less than Annie’s.
The information provided regarding the weight of the apple and its costs can be used to support my answer.
Page 117 Exercise 1 Answer
Given
Meili going to pick the apple and between the apples.
Which orchard should mei li choose?
We simply found out what is the price per one lb of apples. After we found that, we simply had to compare the results, the one that is cheaper is obviously the one she should pick.
We simply found out what is the price per one lb of apples. After we found that, we simply had to compare the results, the one that is cheaper is obviously the one she should pick.
Page 118 Question 1 Answer
Given
How can compare relationship proportional in different ways?
Proportional relationships can be represented by tables, graphs and equations.
We can find the unit rate for each relation and then compare them.
For all three representations, the unit rate is the value of the dependent variable when the independent variable is equal to 1.
Proportional relationships can be represented by tables, graphs and equations.
We can find the unit rate for each relation and then compare them.
For all three representations, the unit rate is the value of the dependent variable when the independent variable is equal to 1.
Page 118 Exercise 1 Answer
Given
The equation is y = 2.5x
Who makes birds at a faster rate?
As we can see from the graph, Marlo makes 2 origami birds in 10 minutes, and we simply have to make an equation from this and calculate how much he needs to make 1 bird.
2y = 10x
Divide both side of the equation by 2.
y = 5x
This means that josh makes twice as many origami birds as Marlo makes.
Josh makes them faster.
Page 118 Exercise 1 Answer
Given
The equation is y = 2.5x
How do you lines compare.?
As we can see from the graph, marlo makes 2 origami birds in 10 minutes, and we simply have to make an equation from this and calculate how much he needs to make 1 bird.
This means that josh makes twice as many origami birds as marlo makes.
Josh makes them faster.
Page 120 Exercise 1 Answer
Given
How can compare relationship proportional in different ways?
Proportional relationships can be represented by tables, graphs and equations.
We can find the unit rate for each relation and then compare them.
For all three representations, the unit rate is the value of the dependent variable when the independent variable is equal to 1.
Proportional relationships can be represented by tables, graphs and equations.
We can find the unit rate for each relation and then compare them.
For all three representations, the unit rate is the value of the dependent variable when the independent variable is equal to 1.
Page 120 Exercise 2 Answer
Given
Find the unit of rate or constant ?
We simply have to read from the graph for which ever of the values on the axis we need.
For example if the unit of hours is on the x-axis than we simply have to put that into the relation with the value that is on the y-axis.
We can find the unit rate or constant of proportionality for a relationship represented in a graph by:
Simply reading from the graph for which ever of the values on the axis we need.
For example if the unit of hours is on the x-axis than we simply have to put that into the relation with the value that is on the y-axis
Page 120 Exercise 3 Answer
Given
Why can you use the constant of proportionality with any representation ?
We can use constant of proportionality with any representation because we can find the unit rate or the constant from the any data that we are given.
We can use constant of proportionality with any representation because we can find the unit rate or the constant from the any data that we are given.
Page 120 Exercise 4 Answer
Given
The points are (0,0) and (4,24)
Who earn more per hour ?
We can simply graph both functions and see which of them makes more money
On the graph we can see function for Amanda and function for petra.
From the graph we can see that Amanda earns more money per hour
Amanda earns more money per hour.
Page 121 Exercise 6 Answer
Given
Find the unit of rate for Sam and bobby?
Who cycled faster?
First we have to find the unit rate for Sam.
Since we can see from the table that he can cycle at 20 miles in 2 hours we simply have to divided the number of miles with hours to find out how much he cycles in one hour.
20 ÷ 2 = 10
He can cycle at speed of 10mi/h
Now to find out the unit rate for bobby we are going to use points (2,18) and (4,36)
Again we simply have to divide miles with the hours to find out the unit rate for bobby.
18 ÷ 2 = 9
36 ÷ 4 = 9
We can see that bobby can cycle at speed of 9mi/h.
Sam can cycle faster.
Page 121 Exercise 7 Answer
Given
y = 5x the equation y is amount of money and x is the selling pizza. Which pizzeria makes more money per pizza?
We are simply going to divide the number of pizzas sold for Leo’s pizza so we can simply compare the results.
The first point that we can see on the graph is (2,24) and we are going to use that point to find the unit rate for him.
24 ÷ 2 = 12
This means that Leo’s pizza makes money by the equation y = 12x
We can simply compare this result to the unit rate of Pauli’s pizzeria with the rate of Leo’s pizza.
15x > 12x
This means that Pauli’s pizzeria takes in more money per pizza.
Pauli’s pizzeria takes in more money per pizza.
Page 122 Exercise 9 Answer
The table given shows the relationship between the number of miles Manuel walks and the amount of money he will raise. Petra will earn $15 for each mile that she walks.
We have to find the quantities to find the unit rate in order to compare the proportional relationship.
When there is a relationship between two variables, and the ratio of the two variables are equivalent, then it is known as proportional relationship.
We are given the data regarding the relationship between the number of miles Manuel walks and the amount of money he will raise
If we have to compare the proportional relationships, we will use the quantities Money Raised and the Miles Walked.
On doing so, we can find the amount of money earned for each mile which is unit rate.
The quantities that we should use to find the unit rate are Money Raised and the Miles Walked so that the proportional relationships can be compared.
The table given shows the relationship between the number of miles Manuel walks and the amount of money he will raise. Petra will earn $15 for each mile that she walks.
We have to compare the amount of money raised per mile by the three people.
In order to calculate the money raised per mile, we will have to divide the money raised by the miles walked by considering the values given from the table.
We will first calculate for Manuel as below:
\(\frac{45}{3}=15\)Thus, Manuel gets the amount $15 for each mile walked.
It is already given that Petra earns $15 for every mile, which is the same as Manuel.
So, we can express amount earned by Petra and Manuel by y = 15x
The equation for the money raised by Beth is given as y = 20x
Now we compare the two equations,
15x < 20x
This concludes that Beth earns the maximum amount of money for per mile walked.
On comparing the money raised by the three people for every mile, Beth earns the most.