SOLUTION: Twenty-two years ago Jake was twice older than Tom. Three times Tom's age now is 16 more than twice Jake's age now. How old were they 22 years ago?

Question 1113162: Twenty-two years ago Jake was twice older than Tom. Three times Tom's age now is 16 more than twice Jake's age now. How old were they 22 years ago?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
let j = Jake's present age
let t = Tom's
Write an equation for each statement
:
Twenty-two years ago Jake was twice older than Tom.
j-22 = 2(t-22)
j - 22 = 2t - 44
j = 2t - 44 + 22
j = 2t - 22
Three times Tom's age now is 16 more than twice Jake's age now.
3t = 2j+16
replace j with (2t-22)
3t = 2(2t-22) + 16
3t = 4t - 44 + 16
3t = 4t - 28
28 = 4t - 3t
t = 28 yrs is Tom's age
then
j = 2(28)- 22
j = 56 - 22
j = 34 yrs is Jake's age
:
How old were they 22 years ago?
t: 28 - 22 = 6 yrs was Tom
j: 34 - 22 = 12 yrs was Jake
RELATED QUESTIONS
Five years ago, Jake's age was one less than half his age now. How old is Jake... (answered by josgarithmetic)

jake is 5 years older than his sister three years ago jake was twice his sisters age how... (answered by stanbon)

this year, jake is 5 years older than his sister. three years ago, jake was twice his... (answered by josgarithmetic,Theo)

Four years ago, the sum of the ages of Tom and Dick was 45. Six years from now, twice... (answered by richwmiller)

michael is 4 years older than tom. 5 years ago michael was twice toms age how old is tom... (answered by ankor@dixie-net.com)

Michael is 3 years older than tome. 5 years ago Michael was twice Tom's age. How old is... (answered by stanbon)

Jake is five years older than laura. Four years ago jake was twice as old as laura was... (answered by lwsshak3)

If Jake were 2 years older, he would be twice as old as Tom. If Jake is 16 now, how old... (answered by ikleyn)

This year, Jake is 5 years older than his sister. Three years ago, Jake was twice his... (answered by DrBeeee)