SOLUTION: six years ago, jim was four times as old as fe. in four years, he would be twice as old as fe. how old are they now?

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Question 620699: six years ago, jim was four times as old as fe. in four years, he would be twice as old as fe. how old are they now?
Found 2 solutions by Maths68, dragonwalker:
Answer by Maths68(1474) About Me  (Show Source):
You can put this solution on YOUR website!
Let
Present age of Jim = j years old
Present age of Fe = f years old


six years ago
Jim was = j-6 years old
Fe was = f-6 years old

Then

Jim was four times as old as Fe
j-6=4(f-6)
j-6=4f-24
j=4f-24+6
j=4f-18...................(1)

In four years
Jim will be = j+4 years old
Fe will be = f+4 years old

Then

Jim would be twice as old as Fe
j+4=2(f+4)
j+4=2f+8
j=2f+8-4
j=2f+4.............(2)
Put the value of j from (1) to (2)
4f-18=2f+4
4f-2f=4+18
2f=22
f=22/2
f=11

Put the value of f in (1)
j=4f-18...................(1)
j=4(11)-18
j=44-18
j=26


Present age of Jim = j = 26 years old
Present age of Fe = f = 11 years old

Answer by dragonwalker(73) About Me  (Show Source):
You can put this solution on YOUR website!
okay, so let us call Fe's age at this time 'f'
So six years ago Fe would have been f-6
and Jim was her age times 4 which can be written 4(f-6)
In four years time Fe will be f+4 and Jim will be 2(f+4)
It can also be written that in four years time Jim will be ten years older than he was six years ago
As six years ago he was 4(f-6) in four years time he will be = 4(f-6) + 10
So in four years time Jim is 2(f+4) but also 4(f-6)+10
So:
4(f-6)+10 = 2(f+4)
solve for f:
4f - 24 + 10 = 2f + 8
rearrange and remember to change the sign if you move a number to the other side of the equation:
4f - 2f = 8 + 24 - 10
2f = 22
divide both sides by 2 to change 2f to f
2f/2 = 22/2
f = 11
So Fe is currently 11 years old. In four years she will be 15 and Jim will be twice this so he will be 30. So at this time he is 30 - 4 = 26.
To check we should look at how old they were 6 years ago:
Fe would have been 11-6 = 5 and Jim would have been 26-6=20 which is indeed 4 times as old as Fe at that time.
The key with these questions is to find a way to write someone's age at a particular time in two different ways and as a function of the other person's age, in this case the age of Jim in four years time in relation to Fe's age. By doing this you can make each formula equal to each other and then solve for the other person's age. In this case Fe's. Then solve and check.