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.

  • wuphysics87
    3•3 months ago

    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.

    • @drawerairOP
      1•3 months ago

      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
        1•3 months ago

        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