SOLUTION: pat is 6 years older than his friend gary. four years ago gary's age was 7 more than half of pat's age. what are their present ages?

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Question 632823: pat is 6 years older than his friend gary. four years ago gary's age was 7 more than half of pat's age. what are their present ages?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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let p = Pat's present age
let g = Gary's
:
Write an equation for each statement
:
pat is 6 years older than his friend gary.
p = g+6
:
four years ago gary's age was 7 more than half of pat's age.
g - 4 = .5(p-4) + 7
g - 4 = .5p - 2 + 7
g = .5p + 5 + 4
g = .5p + 9
Replace p with (g+6), find g
g = .5(g+6) + 9
g = .5g + 3 + 9
g - .5g = 12
.5g = 12
multiply both side by 2
g = 24 yrs is Gary's present age
then
24 + 6 = 30 is Pat's present age
:
:
Check this in the 2nd equation
24 - 4 = .5(30-4) + 7
20 = .5(26) + 7
20 = 13 + 7; confirms of our answers of Pat is 30, Gary is 24