SOLUTION: Four times Polly’s present age is 4 more than eight times Olive’s age 2 years ago. Three times Olive’s age is 3 more than twice what Polly’s age was 4 years ago. Find their

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: Four times Polly’s present age is 4 more than eight times Olive’s age 2 years ago. Three times Olive’s age is 3 more than twice what Polly’s age was 4 years ago. Find their      Log On


   

Question 1187418: Four times Polly’s present age is 4 more than eight times Olive’s age 2 years ago. Three times Olive’s age is 3 more than twice what Polly’s age was 4 years ago. Find their present ages.
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


Define some variables...

Let x = Olive's current age
Let y = Polly's current age

... and translate each given piece of information directly into an algebraic equation.

Four times Polly’s present age is 4 more than eight times Olive’s age 2 years ago.

Polly's present age is y; Olive's age 2 years ago was x-2:
4y=8%28x-2%29%2B4
4y=8x-16%2B4
4y=8x-12
y=2x-3 [1]

Three times Olive’s age is 3 more than twice what Polly’s age was 4 years ago.

Olive's age now is x; Polly's age 4 years ago was y-4:
3x=2%28y-4%29%2B3
3x=2y-8%2B3
3x=2y-5 [2]

With the two equations [1] and [2] in those forms, a solution using substitution seems the way to go. Substitute [1] in [2]:

3x+=+2%282x-3%29-5

I'll let you finish. Solve that equation for x, then substitute the value of x in [1] to find y.