Exercise 4 Page 48

Practice makes perfect

a First, let's try to write the total cost of the renovation without using any mathematical symbols. We know it consists of two parts: the cost of the white paint and the cost of the blue paint.

(Cost of white * Number of white cans) + (Cost of blue * Number of blue cans) Total cost

Our variable must be x because it is the only variable included in the list. If we let x be the number of cans of white paint, then we have x fewer than 5 cans of blue paint.

White cans:& x Blue cans:& 5- x

We also know that white paint costs $24 per can and blue paint costs $28 per can. We can now write total costs for each color of paint. White paint:& 24x Blue paint:& 28(5-x) If we add these these two expressions, we get the total cost, which is $132. 24x+28(5-x)=132

b Before we can consider how much we saved by switching colors, we need to find the number of cans we purchased for the current color configuration. We can do that by solving the equation we wrote in Part A.

24x+28(5-x)=132

Distr

Distribute 28

24x+140-28x=132

▼

Solve for x

SubTerm

Subtract term

-4x+140=132

SubEqn

LHS-140=RHS-140

-4x=-8

MultEqn

LHS * (-1)=RHS* (-1)

4x=8

DivEqn

.LHS /4.=.RHS /4.

x=2

This means that we bought 2 cans of white paint to paint the dining room and 3 cans of blue paint to paint the living room. Let's see what happens if we swap the rooms. cc Before swap & After swap White cans:2 & White cans:3 Blue cans:3 & Blue cans:2 We would need to buy 3 cans of white paint and 2 cans of blue paint. Let's evaluate their total cost, keeping in mind that white and blue paint cost $ 24 and $ 28 per can, respectively.

3*24+2*28

Multiply

72+56

AddTerms

Add terms

128

This paint job would have only cost us $128, saving us 132-128=4 dollars.

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Exercise 4 Page 48

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