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Math Help - Simultaneous equation help

  1. #1
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    Simultaneous equation help

    Here is the question:

    I ate 4 plates of green bananas and bought 10 pounds of dried beans. My weight (including the beans) had increased by 10%. I quickly went on a diet and returned to my original weight. Next time I ate twice as many plates of bananas and bought 10 pounds of maize flour. I weighed myself (including flour) and found my weight had increased by 11%. What was my original weight?

    This is what I have so far:

    1.10x = x + a + 10
    1.11x = x + 2a + 10

    I'm unsure on how to proceed. I've tried lots of different ways but none of them make any sense.

    Thanks for any help.
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  2. #2
    MHF Contributor
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    Quote Originally Posted by preid View Post
    I ate 4 plates of green bananas and bought 10 pounds of dried beans. My weight (including the beans) had increased by 10%. I quickly went on a diet and returned to my original weight. Next time I ate twice as many plates of bananas and bought 10 pounds of maize flour. I weighed myself (including flour) and found my weight had increased by 11%. What was my original weight?

    This is what I have so far:

    1.10x = x + a + 10
    1.11x = x + 2a + 10
    For what do "x" and "a" stand? I think you have defined "x" to be "my original weight" and "a" to be "the weight of the food I ate" or "the weight added by four plates of fruit". If so, your equations look fine.

    Quote Originally Posted by preid View Post
    I'm unsure on how to proceed.
    You have created a "system" of equations. There are many methods for solving a system of linear equations, but I would suggest simplifying and then using "addition".

    First, study a few online lessons to learn the basics. Then:

    . . . . .1.10x = 1x + 1a + 10
    . . . . .1.11x = 1x + 2a + 10

    . . . . .0.10x = 1a + 10
    . . . . .0.11x = 2a +10

    . . . . .10x = 100a + 1000
    . . . . .11x = 200a + 1000

    Multiplying the first equation by -2, you get:

    . . . . .-20x = -200a - 2000
    . . . . ..11x = .200a + 1000

    Add down, and solve for the value of x. Then back-substitute to solve for the value of a.

    Have fun!
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