SOLUTION: HELP! Latoya is twice as old as her cousin was 3 years ago. If the sum of their ages now is 15, how old is each one of them?

Question 26872: HELP!
Latoya is twice as old as her cousin was 3 years ago. If the sum of their ages now is 15, how old is each one of them?
Found 2 solutions by bmauger, Paul:
Answer by bmauger(101) (Show Source): You can put this solution on YOUR website!
This is a matter of converting English into algebra, so let's look at it word by word.
"Latoya" - let's create the variable L to stand for Latoya's age
"is" - means "="
"twice as old as" means we will be multiplying by 2.
"her cousin" - we need a new variable C to represent her cousin's age
"was three years ago" - 3 years ago means we will have to subtract 3
So our first sentence boils down to "Latoya (L) is (=) twice as old as (2 times) her cousin (C) three years ago (-3)" or:

The second part says:
"The sum of" - means we'll be adding together
"their ages now" - L & C
"is" - still means equals
"15" - 15
This translates to:

Now you have two equations, that you can solve either through elimination, substitution, graphing, or any other way you've been taught to solve for the ages of each L & C.
Answer by Paul(988) (Show Source): You can put this solution on YOUR website!
LEt her cousin's age be x
Let her age be 2x
Now she was Twice as old as her cousin was 3 years age so.
2(x-3)

2(x-3)+x=15
2x-6+x=15
3x=21
x=7

2(7-3)
2(4)=8

Hence, Latoya is 8 years old and her cousin is 7 years old.
Paul.

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