Question 893016
x = daughter's age now
50 - x = mother's age now {sum of ages is 50}


x - 5 = daughter's age five years ago {subtracted 5 from age now}
45 - x = mother's age five years ago {subtracted 5 from age now}


45 - x = 7(x - 5) {five years ago the mother was equal to 7 times the daughter}
45 - x = 7x - 35 {used distributive property}
80 = 8x {added 35 and added x to each side}
x = 10 {divided each side by 8}
50 - x = 40 {substituted 10, in for x, into 50 - x}


daughter is 10
mother is 40
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