Advanced Algebra

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

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  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

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  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

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  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.

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  4. I agree with you.

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