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.

- anonymous

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- anonymous

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.

- anonymous

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

- anonymous

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

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- anonymous

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

- anonymous

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

- anonymous

Yes...

- anonymous

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

- anonymous

right...

- anonymous

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

- anonymous

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

- anonymous

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

- anonymous

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!!

- anonymous

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

- anonymous

5 weeks would be -120, right?

- anonymous

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

- anonymous

yep, you're right...

- anonymous

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

- anonymous

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.

- anonymous

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

- anonymous

I agree :(

- anonymous

lol.

- anonymous

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.

- anonymous

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

- anonymous

DEFIANTLY best response. :)

- anonymous

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.

- anonymous

Good luck :) Gotta run...

- anonymous

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

- anonymous

Yep :) It all worked out...

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