SOLUTION: If Rachel was 2 years older, she would be half of Kate's age. If Rachel was two years older, the sum of their ages would be 60.

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Question 1102456: If Rachel was 2 years older, she would be half of Kate's age. If Rachel was two years older, the sum of their ages would be 60.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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Rachel was 2 years older, she would be half of Kate's age.
If Rachel was two years older, the sum of their ages would be 60.
:
Write an equation for each statement
" Rachel was 2 years older, she would be half of Kate's age."
r + 2 = 1%2F2k
get rid of the fraction, multiply by 2
2r + 4 = k
:
" If Rachel was two years older, the sum of their ages would be 60."
r + 2 + k = 60
replace k with (2r+4), from the 1st statement
r + 2 + 2r + 4 = 60
3r + 6 = 60
3r = 60 - 6
3r = 54
r = 54/3
r = 18 yr is Rachel's age
therefore
k = 2(18) + 4
k = 36 + 4
k = 40 yrs is Kate's age
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You can confirm this using the ages in both statements