SOLUTION: A man will be 52 in 7 years and his daughter is currently 1/5 his age. How old will they each be when she will be 1/4 his age? We figured out she is 9 now and he is 45 and the answ

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Question 1000009: A man will be 52 in 7 years and his daughter is currently 1/5 his age. How old will they each be when she will be 1/4 his age? We figured out she is 9 now and he is 45 and the answer is she will be 12 and he will be 48 but how does this work mathematically?
Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
D=daughter's age; M=man's age=5D
X=number of years until daughter is 1/4 Father's age
.
D%2BX=%281%2F4%29%28M%2BX%29
D%2BX=%281%2F4%29%285D%2BX%29
4%28D%2BX%29=5D%2BX
4D%2B4X=5D%2BX
3X=D
X=D%2F3
.
When we calculate the father's age (52-7=45) is 45,
we know the daughter is currently (45/5=9) 9 years old.
So X=D/3=9/3=3 and the daughter will be 1/4 as old in 3 years:
.
CHECK:
D%2BX=%281%2F4%29%28M%2BX%29
9%2B3=%281%2F4%29%2845%2B3%29
12=%281%2F4%29%2848%29
12=12