Rudolph borrowed $650 from his parents to make some repairs on his car. He promised to repay the loan by giving his parents at least $76 from his paycheck each week. If x represents the number of weeks, which linear inequality represents the amount of debt Rudolph has remaining?

Question

Rudolph borrowed $650 from his parents to make some repairs on his car. He promised to repay the loan by giving his parents at least $76 from his paycheck each week. If x represents the number of weeks, which linear inequality represents the amount of debt Rudolph has remaining?

y ≤ $76x + $650
y ≥ $76x + $650
y ≤ $76x - $650
y ≥ $76x - $650

My answer is number 3

If it was 5 weeks it would be 5 * 76 - 650 or $270 left to pay

Answer 1

debt after 1 week = 650 - 76(1)

debt after 2 weeks = 650 - 76(2)
debt after x weeks = 650 - 76(x)

so equation for debt remaining, if y is the debt:
y ≥ 650 - 76x

I don't see that choice, do you have a typo?

You said: "If it was 5 weeks it would be 5 * 76 - 650 or $270 left to pay"
5*7 - 650 = -270 , not 270
That's why my inequality is correct

Answer 2

I believe #4 is correct. The original balance in Rudolph's account is -650.

Using 76x-650, you are correct that the balance in the account after 5 weeks is -270. But, suppose he paid $80 each week. Then the balance would be 5*80-650 = -250. But -250 >= -270.

Actually, I would have said that the original debt is 650, and at least 76 is subtracted each week, making the remaining debt

y <= 650 - 76x

Answer 3

Reiny, there is no typo because what you put is what I would have said but based on the choices offered it's not that easy.

Answer 4

I agree with you.

Answer 5

To determine the linear inequality that represents the amount of debt Rudolph has remaining, we need to consider the given information.

Rudolph borrowed $650 from his parents and promised to repay the loan by giving them at least $76 from his paycheck each week.

Let's break it down step by step:

1. The amount of debt Rudolph has remaining can be represented by the variable y.

2. The number of weeks can be represented by the variable x.

3. Rudolph repays $76 from his paycheck each week, so the amount paid off after x weeks is 76x.

4. To find the remaining debt, we subtract the amount paid off from the initial loan amount of $650. So, the equation for the remaining debt is 650 - 76x.

However, we are looking for a linear inequality that represents the amount of debt Rudolph has remaining, not just the equation.

Since Rudolph must repay at least $76 each week, the amount of debt remaining (y) can be less than or equal to (≤) the equation, resulting in the correct option y ≤ $76x + $650.

Therefore, the correct linear inequality that represents the amount of debt Rudolph has remaining is y ≤ $76x + $650.