## 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.

1. JakeV8

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

wait, that might have an error in it... lemme double check

3. AGummiBear55

okay... I'm a little confused... lol.

4. JakeV8

I think that's right... but guessing stinks. Let's think about it :)

5. JakeV8

he will pay back at least \$65 per week, so the amount paid back each week is >= 65x Does that make sense?

6. AGummiBear55

Yes...

7. JakeV8

So, if he starts owing 445, and he pays back exactly 65 per week, then it would be:: 445 - 65x = y

8. AGummiBear55

right...

9. JakeV8

But that's the most he could have left... if he pays more, y will be smaller.

10. JakeV8

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

This is a little tricky, isn't it? :)

12. AGummiBear55

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

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

5 weeks would be -120, right?

15. JakeV8

weeks y must be less than or equal... 5 445 - 325 = 120 6 445 - 390 = 55

16. JakeV8

yep, you're right...

17. JakeV8

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

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

okay... I'm kinda getting you but it's still a little confusing... :/

20. JakeV8

I agree :(

21. AGummiBear55

lol.

22. JakeV8

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

AHHH!!! I GET IT!!! :O :D Thankkkkkk you!!!!

24. AGummiBear55

DEFIANTLY best response. :)

25. JakeV8

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

Good luck :) Gotta run...

27. AGummiBear55

haha... well I'm glad it made sense to you because then it made sense to me. :)

28. JakeV8

Yep :) It all worked out...