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LeMat
Lv 4
LeMat asked in Science & MathematicsMathematics · 1 decade ago

Quick calculation puzzle?

Hi everyone,

This isn't a homework problem; I'm way too old to be doing math assignments. :)

I'm doing a kind of mini-investigation. Say somebody wanted to arrive at the final figure $3,269.23, and they had to add two numbers together to do it.

If that person chose $2,043.27 and $1,225.96, what process did he use to come up with that result? Neither number is a nice, round percentage of the final figure, but $1,225.96 IS 60% of $2,043.27.

What process or calculation did this guy use to decide on these two numbers? If $1,225.96 is 60% of $2,043.27, what relationship do these numbers have with $3,269.23 (other than that number is their sum)?

Update:

Many thanks, guys.

It was "b = c/1.6 = 5c/8" that got me over the hump. I wasn't concerned with the relationship between the two smaller numbers, but rather in what way those numbers were not arbitrarily chosen vis-a-vis the larger number.

In the result, you helped me solve the puzzle! The guy took the larger number he wanted to reach, and chose his two other numbers by:

1) dividing the large number by 80; and

2) multiplying the result by 50, and then by 30.

Thanks a lot Jared! You saved the day!

2 Answers

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  • ?
    1 decade ago
    Favorite Answer

    In this case, you have two equations.

    We'll call price 1 = x, and price 2 = y.

    So we have x + y = 3269.23

    And if you want x to be 60% of y, you have:

    x = 0.6 * y.

    In this case you can use the two equations to solve for x and y.

    x + y = 3269.23

    .6y + y = 3269.23

    1.6y = 3269.23

    y = 2043.27.

    x = .6y

    x = .6 * 2043.27

    x = 1225.96.

    So that's how you get the two prices.

  • ?
    1 decade ago

    a + b = c

    a = .6b

    .6b + b = c

    1.6b = c

    b = c/1.6 = 5c/8

    or

    b = a/.6 = 5a/3

    a + 5a/3 = c

    8a/3 = c

    a = 3c/8

    Hope this helps

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