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