SOLUTION: Lisa is 1/3 the age of Sally. 6 years ago Lisa was 1/9 the age of Sally. How old is Lisa and How old is Sally? Thank you. Please show step for step. I need help

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Question 46232: Lisa is 1/3 the age of Sally. 6 years ago Lisa was 1/9 the age of Sally. How old is Lisa and How old is Sally? Thank you. Please show step for step. I need help
Found 2 solutions by longjonsilver, wuwei96815:
Answer by longjonsilver(2297) (Show Source):
You can put this solution on YOUR website!
OK, this is straight forward really. Just need to start correctly with a definition.

Let x be the age of Lisa NOW.
Let y be the age of Sally NOW.
As Sally is 3 times older, then --> y = 3x

6 years ago, the ages of the 2 were:
Lisa: x-6 and
Sally: y-6

And Sally's age then was 9 times larger than Lisa's. So
(y-6) = 9(x-6)
y-6 = 9x-54
y = 9x-48

So we have 2 equations:
y = 3x --> eqn 1 and
y = 9x-48 --> eqn2

Now we have 2 equations to solve. There are a few ways of solving them. This is one:

sub eqn1 into eqn2:
3x = 9x-48
0 = 6x-48
48 = 6x
x = 48/6
x = 8

So Lisa is 8 years old now and so Sally is 24 years old.
and 6 years ago, Lisa was 2 and Sally 18... a difference of 9 times.

jon.

Answer by wuwei96815(245) (Show Source):
You can put this solution on YOUR website!
I found this problem difficult to solve.

Let x=Sally's age
Then 1/3x=Lisa's age

Six years ago Sally's age = x-6 and Lisa's age = 1/9(x-6)

Lisa's present age minus 6 years should = her age six years ago.
1/3x-6 = 1/9(x-6)
Remove the parenthesis.
1/3x-6 = 1/9x-6/9
Combining like terms.
1/3x-1/9x = 6-6/9
Using common denominators.
6/27x = 48/9
Divide both sides by 6/27.
x = 48/9 divided by 6/27 = 24

Sally is 24 and Lisa is 1/3 of 24 or 8. Six years ago Sally was 18 and Lisa was 2.

A tough problem?