SOLUTION: mike's age is 3/4 of mary's age. In 5 years, Mike's age will be 7/9 mary's age, how old is mike now?

Question 338583: mike's age is 3/4 of mary's age. In 5 years, Mike's age will be 7/9 mary's age, how old is mike now?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
let m = Mary's present age
let k = Mike's present age
:
Write an equation for each statement:
:
Mike's age is 3/4 of Mary's age.
k = m
we can handle this as a decimal
k = .75m
:
In 5 years, Mike's age will be 7/9 Mary's age,
k + 5 = (m+5)
Multiply both sides by 9
9(k+5) = 7(m + 5)
9k + 45 = 7m + 35
9k = 7m + 35 - 45
9k = 7m - 10
Replace k with .75m
9(.75m) = 7m - 10
6.75m = 7m - 10
6.75m - 7m = -10
-.25m = -10
m =
m = +40 is Mary's present age
then
k = .75(40)
k = 30 is Mike's present age
:
:
Check our solutions in the statement:
"In 5 years, Mike's age will be 7/9 Mary's age"
30 + 5 = (40+5)
35 = (45)
35 = 7*5

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