Question

Zyan’s apartment building has a washing machine that uses a card for payment. There is $50 on the card right now, and her family keeps a minimum balance of at least $10 on the card. Each load of laundry costs $1.50. How many loads of laundry can Zyan’s family do and still have at least $10 on the card?
Write an inequality to represent the situation. Use x to represent the number of loads of laundry Zyan's family does.

Answer 1

To represent the situation using an inequality, we first need to set up the total balance after doing \(x\) loads of laundry.

Starting with a balance of $50, if each load of laundry costs $1.50, then after doing \(x\) loads, the total cost will be \(1.50x\).

Zyan's family wants to maintain a minimum balance of $10 on the card, so we can set up the following inequality:

\[
50 - 1.50x \geq 10
\]

This inequality states that after \(x\) loads of laundry, the remaining balance must be greater than or equal to $10.

Next, we can solve for \(x\):

1. Subtract 10 from both sides:
\[
50 - 10 \geq 1.50x
\]
\[
40 \geq 1.50x
\]

2. Divide both sides by 1.50:
\[
\frac{40}{1.50} \geq x
\]
\[
\frac{40}{1.5} \approx 26.67
\]

Since \(x\) represents the number of loads of laundry, we round down to the nearest whole number (as you can't do a fraction of a load). So:

\[
x \leq 26
\]

Thus, Zyan’s family can do a maximum of **26 loads of laundry** while still keeping at least $10 on the card.