SOLUTION: a person said "my age is 8 timea of your age at that times when i was your age".find the present age of son if the sum of there ages is 75

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Question 1041022: a person said "my age is 8 timea of your age at that times when i was your age".find the present age of son if the sum of there ages is 75
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = father's age now
Let +b+ = son's age now
--------------------------
The difference in their ages never changes
It is +a+-+b+
+a+-+%28+a++-+b+%29+=+b+
So, +a-b+ years ago, the father was the
son's age
-----------------
+a+-+b+ years ago, the son was
+b+-+%28+a-b+%29+=+2b+-+a+ yrs old
-----------------
You are given that:
+a+=+8%2A%28+2b+-+a+%29+
+a+=+16b+-+8a+
+9a+=+16b+
(1) +b+=+%28+9%2F16+%29%2Aa+
Also given is:
(2) +a+%2B+b+=+75+
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Substitute (1) into (2)
(2) +a+%2B+%289%2F16%29%2Aa+=+75+
(2) +%28+25%2F16+%29%2Aa+=+75+
(2) +a+=+%28+16%2F25+%29%2A75+
(2) +a+=+48+
and
(2) +a+%2B+b+=+75+
(2) +48+%2B+b+=+75+
(2) +b+=+27+
The father is 48 and the son is 27
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check:
The difference in their ages is +48+-+27+=+21+
When the father was +27+, the son was +27+-+21+=+6+
The father's age is 8 times that:
+6%2A8+=+48+
OK
(1) +b+=+%289%2F16%29%2Aa+
(1) +27+=+%289%2F16%29%2A48+
(1) +27%2F48+=+9%2F16+
(1) +.5625+=+.5625+
OK