Chapter 1, Problem 4CA

a.

To determine

To use the symbols and number to write the equation for the given situation.

Answer to Problem 4CA

24x + 28(5 − x ) = 132

Explanation of Solution

Given:

The cost of 5 cans of paint = $132

Cost of white paint = $24

Cost of blue paint = $28

Calculation:

Given that the number of cans of paint required to paint dining and living room is 5.

Let x be the number of cans of white paint. Let 5 − x be the number of cans of blue paint.

The cost of white paint is $24 and the cost of blue paint is $28.

Therefore, the situation can be modeled as:

24x +28(5 − x ) = 132.

Conclusion:

Therefore, the number of cans in each color can be represented as 24x + 28(5 − x ) = 132.

b.

To determine

To find the cost saved if the colors are switched.

Answer to Problem 4CA

$4

Explanation of Solution

Given:

The cost of 5 cans of paint = $132

Cost of white paint = $24

Cost of blue paint = $28

The colors are switched.

Calculation:

From subpart (a),

  $24x+28\left(5–x\right)=132$

Solve the above equation:

  $24x+28\times 5-28\times x=132$

  $\begin{array}{l}\Rightarrow 24x+\text{ 140}–28x=132\\ \Rightarrow -4x=132-140\\ \Rightarrow 4x=8\\ \Rightarrow x=2\end{array}$

Therefore, the number of cans of white paint is 2 and the number of cans of blue paint is 3.

If the cans are switched,

  $\begin{array}{c}24(3)+28\left(5–3\right)\text{=24(3)+28( 2)}\\ \text{=128}\end{array}$

Therefore, $132-128=4$

Conclusion:

So, $4 can be saved if the cans of paint are switched.