SOLUTION: Ava's mother is 3 times as old as Ava. Her grandmother is twice as old as Ava's mother. The sum of the numbers is 120. How old are Ava, her mother, and her grandmother? I figured

Question 1077375: Ava's mother is 3 times as old as Ava. Her grandmother is twice as old as Ava's mother. The sum of the numbers is 120. How old are Ava, her mother, and her grandmother? I figured out the ages, but have no clue how to write the equation.
Ava is 12.
Mother is 36.
Grandmother is 72.

Found 2 solutions by Boreal, math_helper:
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
ava=x
mother=3x
grandmother=2(3x)=6x
x+3x+6x=120
10x=120
x=12 Ava
3x=36 Mother
6x=72 grandmother
Answer by math_helper(2461) (Show Source): You can put this solution on YOUR website!
Start by assigning a variable to an unknown:
Let A = Ava's age
Then express other unknowns as a relation to this one (or to other assigned variables). For each unknown, you will need to find an independent (meaning not just a previously found equation multiplied by a constant) equation.
Let M = Ava's mother's age
We are given M=3A (eq 1)
Let G = Ava's grandmother's age
We are given G=2M (eq 2)
The 3rd equation comes from the given information about the sum of their ages totaling 120:
A+M+G = 120 (eq 3)
Now, (eq 3) can be written in terms of A alone, by substituting the values from (eq 1) and (eq 2). First though we need to write (eq 2) in terms of A alone:
G=2M, but M=3A, so G=2(3A) = 6A (eq 2')
Now, substituting into (eq 3):
A + M + G = 120
A + (3A) + (6A) = 120
10A = 120
A = 120/10 = 12 �> M=36 �> G=72
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I hope this helps you understand the steps. There are alternate methods to solving, but this problem lends itself to substitution.

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