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 22 : 11 ?

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