math

Madison spent 5/8 of her savings on a microwave oven & a refrigerator. She used 4/7 of the amount she spent to buy the refrigerator. The refrigerator cost $280 more than the microwave oven. How much savings did Madison start with?

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  1. let the amount of her savings be x

    cost of both = (5/8)x
    cost of fridge = (4/7)(5/8)x = (5/14)x

    (5/8)x - (5/14)x = 280
    15x/56 = 280
    15x = 15680
    x = 1045.33

    Here savings were $1053.33

    cost of fridge = ((5/14)(1045.33 = 373.33
    cost of both = (5/8)(1045.33) = 653.33
    difference = 653.33 - 373.33 = 280
    all checks out

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  2. m= microwave
    r= refrigerator
    s= savings

    m+r=5/8s
    r=4/7 x 5/8s=5/14s
    r=5/14s

    m=r-280
    m=5/14s-280

    m + r = 5/8s
    5/14s-280 + 5/14= 5/8s
    5/14s+5/14s-5/8 = 280
    10/112s = 280
    s= 280x112/10
    s= savings = $3,136

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  3. answer = $3,136

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