Question

Karen is seven years older than suzanne.Four years ago,karen was twice as old as suzanne was.How are they now?

Answer 1

Karen age=k
suzanne age=s

karen (k) is (=) 7 years older (+7) than suzanne(s)
k=7+s

four year ago means
s-4 and k-4

four years ago (-4 to all) karen (k) was (=) twice (2 times) suzzane (s)
k-4=2(s-4)
distribute
k-4=2s-8
add 4 to both sides
k=2s-4
we know that k=7+s so subsitute 7+s for k
7+s=2s-4
add 4 to both sides
11+s=2s
subtract s from both sides
11=s

suzanne=11
subsitute 11 for s in k=s+7

k=7+11
k=18


karen=18
suzanne=11

Answer 2

$K-Karen\ age\\S-Suzanne\ age\\K-4-Karen\ age\ 4\ years\ ago\\S-4-Suzanne\ age\ 4\ years\ ago\\\\ \left\{\begin{array}{ccc}K=S+7\\K-4=2(S-4)\end{array}\right\\\left\{\begin{array}{ccc}K=S+7&(1)\\K-4=2S-8&(2)\end{array}\right\\\\subtitute\ (1)\ to\ (2):\\\\(S+7)-4=2S-8\\S+7-4=2S-8\\S+3=2S-8\ \ \ \ |subtract\ 3\ from\ both\ sides\\S=2S-11\ \ \ |subtract\ 2S\ from\ both\ sides\\-S=-11\\\boxed{S=11}$

$Put\ the\ value\ of\ S\ to\ (1):\\\\K=11+7\\\boxed{K=18}\\\\\left\{\begin{array}{ccc}K=18\\S=11\end{array}\right\\\\Answer:\ Karen\ does\ 18\ years\ and\ Susanne\ does\ 11\ years.$