SOLUTION: This problem has me thoroughly stumped: "Mary is 3 years older than John. In three years John's age will be 4/5 of Mary's age. What are their ages now?"

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Question 405061: This problem has me thoroughly stumped:
"Mary is 3 years older than John. In three years John's age will be 4/5 of Mary's age. What are their ages now?"

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let m = Mary's age now
Let j = John's age now
given:
(1) m+=+j+%2B+3
Next is an equation that compares their ages when they are both 3 yrs older
(2) j+%2B+3+=+%284%2F5%29%2A%28m+%2B+3%29
------------------------
(2) 5%2A%28j+%2B+3%29+=+4%2A%28m+%2B+3%29
(2) 5j+%2B+15+=+4m+%2B+12
(2) 4m+-+5j+=+3
and
(1) m+-+j+=+3
Multiply both sides by 5 and subtract
(2) from (1)
(1) 5m+-+5j+=+15
(2) -4m+%2B+5j+=+-3
m+=+12
and, from(1):
m+=+j+%2B+3
12+=+j+%2B+3
j+=+9
Mary is 12 and John is 9
check answer:
(2) j+%2B+3+=+%284%2F5%29%2A%28m+%2B+3%29
(2) 9+%2B+3+=+%284%2F5%29%2A%2812+%2B+3%29
(2) 12+=+%284%2F5%29%2A15
12+=+12
OK
and, also
(1) m+=+j+%2B+3
(1) 12+=+9+%2B+3
12+=+12
OK