Question 338583
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 = {{{3/4}}}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 = {{{7/9}}}(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 = {{{(-10)/(-.25)}}}
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 = {{{7/9}}}(40+5)
35 = {{{7/9}}}(45)
35 = 7*5