SOLUTION: Mike's age is three fourths of Mary's age. In 5 years Mike's age will be seven ninths Mary's age. How old is Mike now? Please help with this problem.

Question 135953: Mike's age is three fourths of Mary's age. In 5 years Mike's age will be seven ninths Mary's age. How old is Mike now? Please help with this problem.
Answer by ptaylor(2198) (Show Source): You can put this solution on YOUR website!
Let x=Mary's age; x+5=Mary's age in five years
And let y=Mike's age; y+5=Mike's age in 5 years
Now we are told the following:
y=(3/4)x---------------------------------eq1
and
(y+5)=(7/9)(x+5) multiply each side by 9
9y+45=7x+35-------------------------------------eq2
substitute y=(3/4)x from eq1 into eq2 and we get:
9(3/4)x+45=7x+35 or
(27/4)x+45=7x+35 subtract 45 and also 7x from each side
(27/4)x-7x+45-45=7x-7x+35-45 collect like terms
(27/4)x-(28/4)x=-10
-x/4=-10 multiply each side by -4
x=40----------------------------------Mary's age now
(3/4)x=(3/4)*40=30---------------------Mike's age now
CK
30+5=(7/9)(40+5)
35=(7/9)*45
35=35

Hope this helps---ptaylor

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