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 ≤ 10
B.
x ≤ 18
C.
x ≥ 18
D.
x ≥ 10
Let's break it down step by step:
1. Sophie wants to buy sneakers costing $130.40
2. She has to repay a loan to her parents in the amount of $100
3. She earns $12.80 per hour babysitting
So, the total amount of money needed to buy the sneakers after repaying the loan is:
$130.40 - $100 = $30.40
Now, let x be the number of hours Sophie needs to work. Since she earns $12.80 per hour, the total amount of money she earns in x hours is 12.80x.
The inequality to represent the situation is:
12.80x ≥ 30.40
Rearranging the inequality:
x ≥ 30.40 / 12.80
x ≥ 2.375
Since Sophie can't work a fraction of an hour, she needs to work at least 3 hours.
Therefore, the correct answer is:
D. x ≥ 10