Question

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.

Answer 1

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.

Answer 2

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

Answer 3

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

Answer 4

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

Answer 5

he will pay back at least $65 per week, so the amount paid back each week is >= 65x

Does that make sense?

Answer 6

Yes...

Answer 7

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

Answer 8

right...

Answer 9

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

Answer 10

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

Answer 11

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

Answer 12

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!!

Answer 13

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

Answer 14

5 weeks would be -120, right?

Answer 15

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

Answer 16

yep, you're right...

Answer 17

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

Answer 18

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.

Answer 19

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

Answer 20

I agree :(

Answer 21

lol.

Answer 22

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.

Answer 23

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

Thankkkkkk you!!!!

Answer 24

DEFIANTLY best response. :)

Answer 25

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.

Answer 26

Good luck :) Gotta run...

Answer 27

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

Answer 28

Yep :) It all worked out...