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

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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) About Me  (Show Source):
You can put this solution on YOUR website!

let Laura’s age be x+and David’s age y
if 5 years ago David was twice as old as Laura, we have
y-5=2%28x-5%29
y=2x-10%2B5
y=2x-5.....eq.1

if next year Laura will be 3%2F5 the age of David, we have
x%2B1=%283%2F5%29%28y%2B1%29
x%2B1=%283%2F5%29y%2B3%2F5
x%2B1-3%2F5=%283%2F5%29y
x%2B2%2F5=%283%2F5%29y
y=%28x%2B2%2F5%29%2F%283%2F5%29
y=%285x%29%2F3+%2B+2%2F3......eq.2

from eq.1 and eq.2 we have
2x-5=%285x%29%2F3+%2B+2%2F3
6x-15=5x+%2B+2
6x-5x=+15%2B+2
x=+17

go to
y=2x-5.....eq.1, substitute x
y=2%2A17-5
y=29

Laura is 17+years old, and David is 29+years old.



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

Description turned into equations:
system%28y-5=2%28x-5%29%2Cx%2B1=%283%2F5%29%28y%2B1%29%29

y-5=2x-10
y=2x-5
-
5x%2B5=3y%2B3
-
Revised Equations
system%282x-y=5%2C5x-3y=-2%29

Or try substituting:
5x-3%282x-5%29=-2
5x-6x%2B15=-2
-x%2B15=-2
x-15=2
highlight%28x=17%29

Back to y, substituting for x,
y=2%2A17-5
y=34-5
highlight%28y=29%29

Answer by greenestamps(13216) About Me  (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:

%28x%2B6%29%2F%282x%2B6%29=3%2F5
3%282x%2B6%29=5%28x%2B6%29
6x%2B18=5x%2B30
x=12

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

----------------------------------------------------------

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?"