Question

1. open response teddy has two piggy banks. the difference in the amount of money between the two banks is no more than $10. one piggy bank has $731 in it. determine the possible amount of money in the other piggy bank. then interpret the solution.

Explanation:

Step1: Define variable for unknown amount

Let $x$ = amount in the other piggy bank.

Step2: Set up absolute value inequality

The difference between amounts is no more than $10$, so:
$$|x - 7.31| \leq 10$$

Step3: Rewrite as compound inequality

$$-10 \leq x - 7.31 \leq 10$$

Step4: Solve for $x$

Add 7.31 to all parts:
$$-10 + 7.31 \leq x \leq 10 + 7.31$$
$$-2.69 \leq x \leq 17.31$$

Step5: Adjust for real-world context

Since money cannot be negative, $x \geq 0$. So:
$$0 \leq x \leq 17.31$$

Answer:

The other piggy bank can have between $\$0$ and $\$17.31$, inclusive. This means the amount of money in the second piggy bank cannot be less than $\$0$ (you can't have negative money) and cannot be more than $\$17.31$, because the difference between it and the $\$7.31$ in the first piggy bank must not exceed $\$10$.