SOLUTION: If Kurt were 10 years older, he would be twice as old as his sister, and their combined ages would be 36. What are the ages of Kurt and his sister? Thanks so much!

Question 241071: If Kurt were 10 years older, he would be twice as old as his sister, and their combined ages would be 36. What are the ages of Kurt and his sister?
Thanks so much!
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
If Kurt were 10 years older, he would be twice as old as his sister, and their
combined ages would be 36.
What are the ages of Kurt and his sister?
:
let k = Kurt's present age
let s = sister's present age
:
Write an equation for each statement:
;
"If Kurt were 10 years older, he would be twice as old as his sister,"
k + 10 = 2(s + 10)
k + 10 = 2s + 20
k = 2s + 20 - 10
k = 2s + 10
;
" and their combined ages would be 36."
(k+10) + (s+10) = 36
k + s + 20 = 36
k + s = 36 - 20
k + s = 16
:
Replace k with (2s+10); find s
2s + 10 + s = 16
3s = 16 - 10
3s = 6
s =
s = 2 yrs is the sister
and
k + 2 = 16
k = 16 - 2
k = 14 yrs is Kurt
:
:
Check solution in the statement:
"If Kurt were 10 years older, he would be twice as old as his sister, "
14 + 10 = 2(2+10)

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