SOLUTION: Maggie, Amy, and Karen are relatives. They have lived a total of 105 years combined. Maggie’s age is 25 years less than three times Karen’s age. Amy’s age is twice the sum o

Question 1166549: Maggie, Amy, and Karen are relatives. They have lived a total of 105 years combined. Maggie’s age is 25 years less
than three times Karen’s age. Amy’s age is twice the sum of Maggie and Karen’s ages. Find the age of each woman.
Answer by ikleyn(52781) (Show Source): You can put this solution on YOUR website!
.


Since the Amy’s age is twice the sum of Maggie and Karen’s ages, 

we conclude that the sum of M and K ages is one third of 105, i.e. 35 years,

and the Amy's age is 35*2 = 70 years.



Next, we have

    M + K = 35,     (1)

    M = 3K - 25     (2)


So, we substitute (2) into (1) by replacing M there, and we get one single equation then

    (3K - 25) + K = 35,

    4K = 35 + 25

    4K = 60


which has the solution  K = 15.

ANSWER. Karen is 15 years old; Maggie is 35-15 = 20 years old; Amy is 70 years old.

Solved.

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