Question 135953
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