SOLUTION: Six years ago, Mrs. Aguilar was 5 times as old as her daughter Agnes. How old is Agnes now if her age is one -third of her mother’s present age?

Algebra ->  Equations -> SOLUTION: Six years ago, Mrs. Aguilar was 5 times as old as her daughter Agnes. How old is Agnes now if her age is one -third of her mother’s present age?       Log On


   

Question 1190170: Six years ago, Mrs. Aguilar was 5 times as old as her daughter Agnes. How old is Agnes now if her age is one -third of her mother’s present age?
Found 3 solutions by josgarithmetic, greenestamps, MathTherapy:
Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
mother m
daughter d
system%28m-6=5%28d-6%29%2Cd=m%2F3%29

m-6=5%28m%2F3-6%29
-
3%28m-6%29=15%28m%2F3-6%29
3m-18=5m-90
-18%2B90=2m
m=45-9
highlight%28m=36%29
Agnes is 1%2F3 of that, so she is highlight%28highlight%2812%29%29.

Answer by greenestamps(13198) About Me  (Show Source):
You can put this solution on YOUR website!


A different setup, using only one variable -- using the information that the mother was 5 times as old as Agnes 6 years ago....

Let x = age of Agnes 6 years ago
Then 5x = age of mother 6 years ago

Their current ages are
x+6 = Agnes
5x+6 = mother

The mother is now 3 times as old as Agnes:

5x+6 = 3(x+6)
5x+6=3x+18
2x=12
x=6

ANSWER: Agnes' age now is x+6=12

CHECK: 5x+6=20+6=36 = 3(12)

Answer by MathTherapy(10551) About Me  (Show Source):
You can put this solution on YOUR website!
Six years ago, Mrs. Aguilar was 5 times as old as her daughter Agnes. How old is Agnes now if her age is one -third of her mother’s present age?
Let Agnes' and her mom's ages, be A and M, respectively

Then we get: M - 6 = 5(A - 6)____M - 6 = 5A - 30____M = 5A - 24 ---- eq (i)

In addition, matrix%281%2C7%2C+A%2C+%22=%22%2C+M%2F3%2C+%22====%3E%22%2C+M%2C+%22=%22%2C+3A%29

               3A = 5A - 24 ----- Substituting 3A for M in eq (i)

          3A - 5A = - 24

             - 2A = - 24

Agnes' age, or