SOLUTION: Five years from now, two times the age of Ms.Emmy will be eight years less than four times the age of her niece three years ago. If Ms.Emmy is 15 years older than her niece, what a

Question 993852: Five years from now, two times the age of Ms.Emmy will be eight years less than four times the age of her niece three years ago. If Ms.Emmy is 15 years older than her niece, what are their present ages?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
let e = Emmy's age
let n = Niece's age
:
Write an equation for each statement, simplify
:
Five years from now, two times the age of Ms.Emmy will be eight years less than four times the age of her niece three years ago.
2(e+5) = 4(n-3) - 8
2e + 10 = 4n - 12 - 8
2e = 4n - 20 - 10
2e = 4n - 30
:
If Ms.Emmy is 15 years older than her niece, what are their present ages?
e = n + 15
:
Replace e with (n+15) in the 1st equation
2(n+15) = 4n - 30
2n + 30 = 4n - 30
30 + 30 = 4n - 2n
60 = 2n
n = 60/2
n = 30 yrs is the niece
then
30 + 15 = 45 yrs is Emmy's age
:
;
Check this in the 1st statement
"Five years from now, two times the age of Ms.Emmy will be eight years less than four times the age of her niece three years ago.
2(45 + 5) = 4(30 - 3) - 8
2(50) = 4(27) - 8
100 = 108 - 8
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