SOLUTION: Hi 5 years ago David was twice as old as Laura. Next year Laura will be 3/5 the age of David. How old are each of them. Thanks

Question 1205551: Hi
5 years ago David was twice as old as Laura. Next year Laura will be 3/5 the age of David. How old are each of them.
Thanks
Found 3 solutions by MathLover1, josgarithmetic, greenestamps:
Answer by MathLover1(20850)   (Show Source): You can put this solution on YOUR website!

let Laura’s age be and David’s age
if years ago David was twice as old as Laura, we have

.....eq.1

if next year Laura will be the age of David, we have

......eq.2

from eq.1 and eq.2 we have

go to
.....eq.1, substitute

Laura is years old, and David is years old.

Answer by josgarithmetic(39630)   (Show Source): You can put this solution on YOUR website!
x, Laura
y, David

Description turned into equations:

-

-
Revised Equations

Or try substituting:

Back to y, substituting for x,

Answer by greenestamps(13216)   (Show Source): You can put this solution on YOUR website!

There are always many different ways to set up a problem for solving using formal algebra. You should always be comfortable with trying different ways, to find a way for which the effort required to solve the problem is as little as possible.

Often, if part of the given information is that one number is n times another, an easy path to the solution is by starting with that information. Try that on this problem....

Let x = Laura's age 5 years ago
Then 2x = David's age 5 years ago

"Next year" is 6 years after "5 years ago", so their ages next year will be x+6 and 2x+6. Laura's age will be 3/5 of David's age then:

ANSWERS: Their current ages are
Laura = x+5 = 12+5 = 17
David = 2x+5 = 2(12)+5 = 24+5 = 29

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Language note....

"each" refers to a single thing -- in this case a single person. So

"How old are they?"

or

"How old is each of them?"

but not

"How old are each of them?"

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