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AGummiBear55

  • 2 years ago

Michael borrowed $445 from his parents to make some repairs on his car. He promised to repay the loan by giving his parents at least $65 from his paycheck each week. Which of the following is not a possible scenario for the amount of debt Michael has remaining? After 3 weeks, Michael is $225 in debt. After 4 weeks, Michael is $200 in debt. After 5 weeks, Michael is $115 in debt. After 6 weeks, Michael is $45 in debt. I know you use: 65x-445<=y... but when I do it it doesn't match up to any of the multiple choice answers.

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  1. JakeV8
    • 2 years ago
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    You just have your inequality mixed up a little... Try: y <= 445 - 65x This means the amount left must be less than or equal the starting 445 - 65 for each week.

  2. JakeV8
    • 2 years ago
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    wait, that might have an error in it... lemme double check

  3. AGummiBear55
    • 2 years ago
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    okay... I'm a little confused... lol.

  4. JakeV8
    • 2 years ago
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    I think that's right... but guessing stinks. Let's think about it :)

  5. JakeV8
    • 2 years ago
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    he will pay back at least $65 per week, so the amount paid back each week is >= 65x Does that make sense?

  6. AGummiBear55
    • 2 years ago
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    Yes...

  7. JakeV8
    • 2 years ago
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    So, if he starts owing 445, and he pays back exactly 65 per week, then it would be:: 445 - 65x = y

  8. AGummiBear55
    • 2 years ago
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    right...

  9. JakeV8
    • 2 years ago
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    But that's the most he could have left... if he pays more, y will be smaller.

  10. JakeV8
    • 2 years ago
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    so it appears that was right :) 445 - 65x >= y if he doesn't pay more, then y will be = 445 - 65x If he pays more, y will be less than 445 - 65x

  11. JakeV8
    • 2 years ago
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    This is a little tricky, isn't it? :)

  12. AGummiBear55
    • 2 years ago
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    Yeah... but I get it so far... it's just when you put all the numbers in and they don't match up to any of the answers I'm given I'm, like, AHH!!

  13. JakeV8
    • 2 years ago
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    So, maybe a table would help: x weeks y, if paying exactly 65 ------- ----------------- 1 445 - 65 = 380 <<< your answer must be less than this 2 445 - 130 = 315 3 445 - 195 = 250 4 445 - 260 = 185

  14. AGummiBear55
    • 2 years ago
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    5 weeks would be -120, right?

  15. JakeV8
    • 2 years ago
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    weeks y must be less than or equal... 5 445 - 325 = 120 6 445 - 390 = 55

  16. JakeV8
    • 2 years ago
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    yep, you're right...

  17. JakeV8
    • 2 years ago
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    take another look at week 4... Week 4 y must be <= 445 - 260, so y <= 185 But your answer for week 4 says y = $200

  18. JakeV8
    • 2 years ago
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    If he pays exactly $65 for 4 weeks, he will still owe 185. But he might pay more and owe less. But there's no way he can pay at least $65 and still owe $200... y must be less than or equal 445 - (4)(65), or less than or equal 185.

  19. AGummiBear55
    • 2 years ago
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    okay... I'm kinda getting you but it's still a little confusing... :/

  20. JakeV8
    • 2 years ago
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    I agree :(

  21. AGummiBear55
    • 2 years ago
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    lol.

  22. JakeV8
    • 2 years ago
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    You basically need to find those pairs for each value of x... that is the most that y could be. If any answer shows y more than your pairs show it, then that's the answer that is impossible, which is what they asked you. I don't know if you like graphing :) but in graph terms, the inequality is bordered by a line that looks like y = 445 - 65x or y = -65x + 445 and since the inequality is a "less than or equal", then the graph would be shaded below that line. So, the answer for week 4 said "y = 200" but that's a point outside your shaded region. All the other answers fall underneath the line and inside the shaded region.

  23. AGummiBear55
    • 2 years ago
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    AHHH!!! I GET IT!!! :O :D Thankkkkkk you!!!!

  24. AGummiBear55
    • 2 years ago
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    DEFIANTLY best response. :)

  25. JakeV8
    • 2 years ago
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    Glad to hear it :) and I'm happy to help... This was confusing... but glad you finally saw it. I thought I saw it quickly, then as you saw, I talked myself into a circle before it made sense again.

  26. JakeV8
    • 2 years ago
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    Good luck :) Gotta run...

  27. AGummiBear55
    • 2 years ago
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    haha... well I'm glad it made sense to you because then it made sense to me. :)

  28. JakeV8
    • 2 years ago
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    Yep :) It all worked out...

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