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If you can answer these problems, I'd highly appreciate it.

  1. There is a total of 62 tennis balls. A long tube can hold 5 balls. A short tube can hold 3 balls. How many tubes are there?
  2. Find the consecutive numbers whose sum is 465.

I'm awarding 35 points, with a Brainliest Answer.

Verified Answer :

mathstudent55
  1. I assume that you must have full tubes of 5 balls and of 2 balls. I also assume you are looking for the least number of tubes.

    To fit the balls in only tubes of 5, you'd need:
    62/5 = 12.4, or more than 12 tubes, but fewer than 13.

    If you used 12 tubes of 5, you'd fit 60 balls. Then one tube of 3 balls would only have 2 balls.

    Try 11 tubes of 5. That fits 55 balls. There are 7 left, but 7 is not divisible by 3.

    Try 10 tubes of 5. That fits 50 balls. There are 12 balls left. 12 is divisible by 3.
    12/3 = 4.

    That means you need 10 tubes of 5 and 4 tubes of 3 to have the smallest number of tubes possible.

    2. If you are looking for 2 consecutive integers, then let the smaller integer be x. The larger integer is x + 1.
    x + x + 1 = 465
    2x + 1 = 465
    2x = 464
    x = 232
    x is the smaller integer, and it is 232. The larger integer is 233.

    Here is a way to solve without using an equation learned in algebra.
    The sum of the two consecutive integers is 465.
    Divide 465/2 = 232.5
    Choose one integer just less than 232.5 and one integer just greater than 232.5.
    Answer: 232 and 233

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