SOLUTION: Amy is 12 years more than half Penny's age in 7 years Amy will be 22 years less than two times Penny's age. What are their ages?

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Question 1114597: Amy is 12 years more than half Penny's age in 7 years Amy will be 22 years less than two times Penny's age. What are their ages?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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let a = Amy's present age
let p = Penny's
:
Write an equation for each statement
:
Amy is 12 years more than half Penny's age
a = 1%2F2p + 12
in 7 years Amy will be 22 years less than two times Penny's age.
a + 7 = 2(p+7) - 22
a = 2p + 14 - 22 - 7
a = 2p - 15
in the first equation, replace a with (2p-15)
2p - 15 = 1%2F2p + 12
2p = 1%2F2p + 12 + 15
2p = 1%2F2p + 27
2p -1%2F2p = 27
1.5p = 27
p = 27%2F1.5
p = 18 yrs is Penny's age
then
a = 2(18) - 15
a = 21 yrs is Amy's age
:
:
Check in the statement
"Amy is 12 years more than half Penny's age
21 = 1%2F2(18) + 12
21 = 9 + 12