SOLUTION: A man is 37 years old and his child's age is 8. How many years ago was the product of their ages 96

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Question 697627: A man is 37 years old and his child's age is 8. How many years ago was the product of their ages 96
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +x+ = that number of years
given:
+%28+37+-+x+%29%2A%28+8+-+x+%29+=+96+
+296+-+8x+-+37x+%2B+x%5E2+=+96+
+x%5E2+-+45x+%2B+200+=+0+
Use quadratic formula
x+=+%28+-b+%2B-+sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29+
+a+=+1+
+b+=+-45+
+c+=+200+
x+=+%28+-%28-45%29+%2B-+sqrt%28+%28-45%29%5E2+-+4%2A1%2A200+%29%29+%2F+%282%2A1%29+
x+=+%28+45+%2B-+sqrt%28+2025+-+800+%29%29+%2F+2+
x+=+%28+45+%2B-+sqrt%28+1225+%29%29+%2F+2+
x+=+%28+45+-+35%29+%2F+2+
+x+=+5+
and also,
+x+=+%28+45+%2B+35+%29+%2F+2+
+x+=+40+
It could not have been 40 yrs ago- The man wasn't born yet.
It must have been 5 years ago
check the answer:
+%28+37+-+x+%29%2A%28+8+-+x+%29+=+96+
+%28+37+-+5+%29%2A%28+8+-+5+%29+=+96+
+32%2A3+=+96+
+96+=+96+
OK