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.

1. a. explain how the parts of the tape diagram represent the story.
2. b. how much does andre’s neighbor pay him each week to mow the lawn?

Explanation:

Step1: Define variables and total

Let $x$ = weekly pay from neighbor. Total saved: $\$40$ over 5 weeks.
Each week's savings: $x - 2$ (pay minus $\$2$ donation).
Total savings equation: $5(x - 2) = 40$

Step2: Solve for weekly savings

Divide both sides by 5:
$\frac{5(x - 2)}{5} = \frac{40}{5}$
$x - 2 = 8$

Step3: Find weekly pay $x$

Add 2 to both sides:
$x - 2 + 2 = 8 + 2$
$x = 10$

Answer:

3a. The total length of the tape diagram ($40$) represents the total $\$40$ Andre needs to save. Each of the 5 equal segments labeled $x-2$ represents the amount Andre saves each week: this is the weekly pay $x$ from his neighbor minus the $\$2$ he donates to the food bank, and there are 5 segments because he takes 5 weeks to reach his goal.
4b. $\$10$