Envision Math Grade 8 Volume 1 Chapter 2 Analyze And Solve Linear Equations
Page 85 Exercise 1 Answer
To represent the relationship between the number of laptops and the total cost, we can draw a bar diagram
The bar diagram will be divided into 10 parts, one part for each computer, and the total length will represent the total cost of $7500.
Since each laptop has the same cost, each part of the bar diagram can be labeled as x, where x represents the cost of 1 laptop.
The diagram for the representation of relationship between the number of laptops and the total cost
The bar diagram will be divided into10
parts, one part for each computer, and the total length will represent the total cost of $7500.
Since each laptop has the same cost, each part of the bar diagram can be labeled as x, where x represents the cost of 1 laptop.
Hence, the equation for the given information is 10x = 7500.
Page 85 Exercise 1 Answer
It is important because we can use one variable for one value.
If each laptop would cost a different than we would have different variables.
It is important because we can use one variable for one value.
If each laptop would cost a different than we would have different variables.
Page 86 Exercise 1 Answer
We need to explain why we can use the same variable to represent the number of placements and to represent the number of napkins.
We have to ease combining the coefficients. So the number of placements and the number of napkins uses the same variable.
We have to ease to combine the coefficients. So the number of placements and the number of napkins uses the same variable.
Page 87 Exercise 2 Answer
We need to explain how does the original price and the sale price relate.
The sale price of the computer screen is $130
The price of the computer before the sale is $200
The computer was sold for 35% off the original price.
The sale price is 100 − 35 = 65% of the given original price.
Page 86 Exercise 1 Answer
Given:
Each necklace costs $9.99
Each bracelet costs $7.99
Total costs $53.94
Page 87 Exercise 2 Answer
Given:
Grocery bill $150
Discount 5%
If something has a discount of 5% that means that they pay 95% of the original price.
Now we can write an equation with 0.95 of the bill and on the right side the price Nat paid.
0.95x = 150
Divide both sides by 0.95
0.95x ÷ 0.95 = 150 ÷ 0.95
x ≈ 157.89
Hence, the grocery bill before the discount was ≈ 157.89
Page 87 Exercise 3 Answer
Given:
\(-\frac{1}{4} d-\frac{2}{5} d=39\)Solve for d
Hence, the value of d is -60.
Given:
−9.7d − (−12.81d) = 8.54
Hence, the value of d is ≈ 2.746.
Page 86 Exercise 1 Answer
Given:
9.99s + 7.99s + 4.6 = 53.94
To find: Can you combine the s terms and 4.6? Explain.
We cannot combine the s terms and 4.6 because there can only be either variables on one side or normal values.
So, we cannot combine terms and 4.6.
Page 88 Exercise 2 Answer
The like terms are recognized in the equation by having the same variable and exponents
Example:
12d + 3d = 24
12d And 3d are like terms.
The like terms are recognized in the equation by having the same variable and exponents.
Page 88 Exercise 3 Answer
Given
\(0.75 s-\frac{5}{8} s=44\)In the given equation first, we rewrite our like terms in fraction form or decimal form.
Both of them need to be written in some form
First we rewrite our like terms in fraction form or decimal form. both of them need to be written in same form and then combined by subtracting the coefficients.
Page 88 Exercise 5 Answer
Given
Total population: 350,000
Decreased population 3%
If we know that the population of a city decreased by 30% and now is 350,000 this means that 350,000 is 0.7 of the population that was 10 years ago.
Therefore, 10 years ago the population of the same city was 500,000.
Page 88 Exercise 6 Answer
Given
−12.2z − 13.4z = −179.2
Therefore, the solution of the given equation is 7.
Page 89 Exercise 7 Answer
The given equation is \(\frac{4}{5} x-\frac{1}{4} x=11\)
We need to solve the given equation and find the value of x
Solving the equation, we get,
The value of x = 20
Page 89 Exercise 8 Answer
The given equation is −0.65x + 0.45x = 5.4
We need to solve the given equation and find the value of x
The value of x = -27
Page 89 Exercise 10 Answer
The given equation is −3.8x − 5.9x = 223.1
We need to solve the given equation and find the value of x
The value of x = -23
Page 89 Exercise 12 Answer
The given equation is \(-\frac{3}{5} x-\frac{7}{10} x+\frac{1}{2} x=-56\)
Solving the equation, we get,
The value of x = 70
Page 90 Exercise 16 Answer
We need to write an equation that can be represented by the bar diagram, then we need to solve the unknown value.
The equation that can be represented by the bar diagram is,
−1.2y − 4.2y = −3.78
The equation that can be represented by the bar diagram is,
−1.2y − 4.2y = −3.78
The value of y = 0.7
Page 90 Exercise 17 Answer
The given equation is \(\frac{2}{3} h-156=3 \frac{13}{24}\)
We need to solve the given equation and find the value of h
Solving the given equation, we get,
The value of h = 239.25
Page 90 Exercise 18 Answer
Given
The total cost of the notebooks and binders was $27.08.
To find/solve
Draw a bar diagram to represent the situations.
Nathan had bought one notebook and one binder in value 0.95 + 5.82 for each class. If we want to find how many classes does Nathan have, we just make an equation with value for each class on one side as variable and the money that he spent on the other side.
0.95x + 5.82x = 27.08
6.77x = 27.08
Now we divide both sides of the equations with the factor next to x.
6.77x/6.77 = 27.08
x = 4
Nathan is taking 4 classes.
Nathan is taking 4 classes.
Page 90 Exercise 20 Answer
Given
A 132 inch board is cut into two pieces. One piece is three time the length of the other.
To find/solve
Draw a bar diagram to represent the situation.
We simply have to divide the bar diagram on two pieces where one piece is exactly 3 times larger than the other piece.
The total length of whole diagram is 132 in
Simply divide the diagram that is total of 132 in, on 2 pieces where one piece is 3 times larger than the other.
Simply divide the diagram that is total of 132 in, on 2 pieces where one piece is 3 times larger than the other.
Given
A 132 inch board is cut into two pieces. One piece is three time the length of the other.
To find/solve
write and solve an equation to find the length of the shorter piece.
If we cut a board in two pieces where one piece is three times the length of the other this means that if we split one whole into four parts with one being three times the other part, this simply means;
\(\frac{4}{4}=\frac{1}{4}+\frac{3}{4}\)So if we know that whole board is 132 inch we can simply multiply this number with value of shorter part which is \(\frac{1}{4}\)
\(\text { 132. } \frac{1}{4}=33\)Shorter part is 33 inches long.
Shorter part is 33 inches long.