Math

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there is $175,000 to award. If the money is awarded to 4 students in a ratio of 1 to 2 to 3 to 4, how much will the largest award be?

How would I solve this ?

  • Math -

    solve for x

    x + 2x + 3x + 4x = 175 000

    then evaluate 4x

  • Math -

    could you explain why you put it into that equation?

  • Math -

    I split the parts into the given ratios of
    1 : 2 : 3 : 4 or
    x : 2x : 3x : 4x
    remember that ratios can be reduced to "lowest terms" by dividing each value by the same number, a common factor.
    In the same way I can build up a ratio by myltiplying each term by the same value
    e.g.
    1:2:3:4
    = 5:10:15:20
    = 100:200:300:400
    or in an infinite number of way.
    So I chose x as my multiplier

    then the 4 parts must add up to 175 000
    x+2x+3x+4x = 175000
    10x = 175000
    x = 17 500

    then 2x = 35 000
    3x = 52 500
    4x = 70 000

    notice that
    17500 : 35000:52500:70000
    = 175:350:525:700
    = 1:2:3:4 and their sum is 175000

  • Math -

    ok
    thank you

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