Sophie earns $12.80 per hour babysitting. She has to repay a loan to her parents in the amount of $100. After repaying the loan, she wants to have at least enough money to buy herself a pair of sneakers costing $130.40. Write an inequality modeling the number of hours, x, Sophie needs to work to have enough money to buy the sneakers.

A.
x ≥ 18
B.
x ≤ 18
C.
x ≥ 10
D.
x ≤ 10

1 answer

Let's break down the problem step by step:

1. Sophie needs to repay a loan of $100 to her parents.
2. She wants to have enough money to buy a pair of sneakers worth $130.40.
3. She earns $12.80 per hour babysitting.
4. Let x represent the number of hours Sophie needs to work to have enough money to buy the sneakers.

The total amount Sophie will receive from working x hours is 12.80x.

After repaying the loan, she will have 12.80x - 100 dollars.

She wants to have at least enough money to buy the sneakers, so we write the inequality:

12.80x - 100 ≥ 130.40

To solve for x:

12.80x - 100 ≥ 130.40
12.80x ≥ 130.40 + 100
12.80x ≥ 230.40
x ≥ 230.40/12.80
x ≥ 18

Therefore, the correct answer is:
A. x ≥ 18