•

Algebra question

I'm thinking re the latest vid of @mindyourdecisions

No need to view his vid. Here's the problem –

Brian has some boxes of paper clips. Some boxes hold 10 clips and some boxes hold 100. He has some paper clips left over. He has 3 more boxes with 100 paper clips than he has boxes with 10 paper clips. He has 2 fewer paper clips left over than he has numbers of boxes with 100 paper clips. What number of paper clips could he have?

let x1 be the number of boxes with 10 clips
x2 be the number of boxes with 100 clips
n be the number of leftover clips

I thought of 100x2 = 10x1 + 300

Is that equation right? Something tells me I shouldn't equate 100x2 to 10x1 plus 300. Something tells me I shouldn't make an equation re number of clips as it isn't explicit in the problem. I'm confused.

3 comments

wuphysics87

•

It's a system of equations. 2 equations, 2 unknowns. The number of boxes of 10. And the number of boxes of 100 are your unknowns. Call these x and y respectively. (Or your x1 x2)

The two equations come from the following conditions:

He has 3 more boxes with 100 paper clips than he has boxes with 10 paper clips.
He has 2 fewer paper clips left over than he has numbers of boxes with 100 paper clips

As an aside. This problem is dumb. Fuck brian. Fuck his paperclips.

drawerair

•

Thanks.

The problem says “Some boxes hold 10 clips and some boxes hold 100. He has some clips left over.” I think it’s a poorly worded problem but let’s just suppose that “some” means 2 minimum. I read a comment that went like “If you’ll say that there are some donuts and I’ll find out there’s only 1 or 0 donut, I’ll be disappointed.” Sensible.

It’s assumed that Brian put clips in boxes as much as possible, so the number of leftovers is less than 10.

x2 = x1 + 3

n = x2 − 2

x2 should be 5 minimum

The total number of clips is 523, 634, 745, 856, 967, 1078 or 1189.

I asked Llama 3.1 (405b), Claude 3.5 sonnet and Chatgpt 4o after I solved it. I edited the problem to improve it. I was curious if any of those could solve it. Claude 3.5 sonnet and Chatgpt 4o did. Llama 3.1 (405b) got 523 but didn’t talk re the other answers. A follow-up of “Are there other answers?” yielded all the 7 answers.

wuphysics87

•

You are getting close. You are getting so many answers because you introduced the variable n. This makes it 2 equations and 3 unknowns. You need to cast the 2nd equation in terms of the number of boxes and the number of paper clips in each box rather than an additional variable. Here's a hint. If:

x1 * 100 = 300 then x1=3

I.e. the total number of paperclips from the 100 paperclip boxes is 300 if there are 3 boxes of them