Question 1114597
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 = {{{1/2}}}p + 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 = {{{1/2}}}p + 12
2p = {{{1/2}}}p + 12 + 15
2p = {{{1/2}}}p + 27
2p -{{{1/2}}}p = 27
1.5p = 27
p = {{{27/1.5}}}
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 = {{{1/2}}}(18) + 12
21 = 9 + 12