Question

andre wants to save $40 to buy a gift for his dad. andre’s neighbor will pay him weekly to mow the lawn, but andre always gives a $2 donation to the food bank in weeks when he earns money. andre calculates that it will take him 5 weeks to earn the money for his dad’s gift. he draws a tape diagram to represent the situation.

tape diagram with 5 parts labeled ( x - 2 ) and total 40

a. complete the statements about how the parts of the tape diagram represent the story.
the (square) equal parts represent the (square) weeks. in each week, andre will earn ( x ) dollars for mowing his neighbor’s lawn and give $ (square) to the food bank, so he will save ( x - 2 ) dollars. in five weeks, he will save a total of $ (square).

b. how much does andre’s neighbor pay him each week to mow the lawn? $ (square)

Explanation:

Part a

1. Looking at the tape diagram, there are 5 equal parts. The problem states it takes 5 weeks, so the 5 equal parts represent the 5 weeks.
2. The problem says Andre gives a $2 donation to the food bank each week he earns money.
3. Since each week he saves \( x - 2 \) dollars and there are 5 weeks, the total saved is \( 5(x - 2) \) or we know from the problem the total he needs to save is $40, so the total saved is $40.

Step 1: Set up the equation

We know that the total amount saved in 5 weeks is $40, and each week he saves \( x - 2 \) dollars. So the equation is \( 5(x - 2)=40 \).

Step 2: Solve for \( x \)

First, divide both sides of the equation by 5: \(\frac{5(x - 2)}{5}=\frac{40}{5}\), which simplifies to \( x - 2 = 8 \).
Then, add 2 to both sides: \( x - 2+2 = 8 + 2 \), so \( x = 10 \).

Answer:

The \(\boldsymbol{5}\) equal parts represent the \(\boldsymbol{5}\) weeks. In each week, Andre will earn \( x \) dollars for mowing his neighbor’s lawn and give $\boldsymbol{2}$ to the food bank, so he will save \( x - 2 \) dollars. In five weeks, he will save a total of $\boldsymbol{40}$ (or \( 5(x - 2) \)).

Part b