Two years ago Pete was three times as old as his cousin Claire. Two years before that, Pete was four times as old as Claire. In how many years will the ratio of their ages be 2 : 1 ?

Guest Sep 8, 2017

#1**0 **

P=pete's age now

c=claire's age now

2 year ago pete was 3times as old as his cousin clarie

p-2=3 times (c-2)

also the ratio is 1:3

2 years before that, pete was 4 times as old as claire

p-4=4 times (c-4)

so solve

p-2=3(c-2)

p-4=4(c-4)

distribute

p-2=3c-6

p-4=4c-16

p-2=3c-6

add 2 to both sides

p=3c-4

p-4=4c-16

add 4 to both sides

p=4c-12

so nowe we have

p=3c-4 and p=4c-12

therefor they are equal

3c-4=p=4c-12

3c-4=4c-12

add 12 to both sides

3c+8=4c

subtract 3c from both sides

8=c

subsitute

p-2=3(c-2)

p-2=3(8-2)

p-2=3(6)

p-2=18

addd 2

p=20

so right now, pete is 20 and claire is 8

so we solve by doing

20+what to 8+what=22 to 11

make fraction

and replace what with x

sipmlify 22/11 into 2/1

multiply both sides by 8+x

20+x=

20+x=2(8+x)

distribute

20+x=16+2x

subtract 16 from both sides

4+x=2x

subtract x from both sides

4=x

the answer is in 4 years

test

20+4=24

8+4=12

24/12=22/11?

2/1=2/1

true

the answer is in 4 years

cowgirlkatie03
Sep 8, 2017

#2**+1 **

Let Claire age 4 years ago = C

Pete's age 4 years ago was =4C

Claire's age 2 years ago was = C+2

Pete's age 2 years ago =4C+2

(4C+2) / (2+C) = 3, solve for C

C = 4 years - Claire age 4 years ago

4 x 4 = 16 years - Pete's age 4 years ago.

4+4 = 8 years - Claire's age today

16+4 = 20 years - Pete's age today

(20 + n)/(8+n) =2, solve for n

n = 4 years from now when they will be 24 and 12, or a ratio of 2:1.

Guest Sep 8, 2017