SOLUTION: Brandon is one year older than three times his brother’s age. The product of their ages is 80. How old is Brandon’s brother?

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Question 1044419: Brandon is one year older than three times his brother’s age. The product
of their ages is 80. How old is Brandon’s brother?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +y+ = Brandon's age
Let +x+ = his brother's age
--------------------------
(1) +y+=+3x+%2B+1+
(2) +y%2Ax+=+80+
------------------
Substitute (1) into (2)
(2) +%28+3x+%2B+1+%29%2Ax+=+80+
(2) +3x%5E2+%2B+x+-+80+=+0+
I'll use the quadratic formula
+x+=+%28+-b+%2B-+sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29+
+a+=+3+
+b+=+1+
+c+=+-80+
--------------
+x+=+%28+-1+%2B-+sqrt%28+1%5E2+-+4%2A3%2A%28-80%29+%29%29+%2F+%282%2A3%29+
+x+=+%28+-1+%2B-+sqrt%28+1+%2B+960+%29%29+%2F+6+
+x+=+%28+-1+%2B-+sqrt%28+961+%29%29+%2F+6+
+x+=+%28+-1+%2B+31+%29+%2F+6+
+x+=+30%2F6+
+x+=+5+
--------------
Brandon's brother is 5 yrs old
---------------------------
check:
(1) +y+=+3x+%2B+1+
(1) +y+=+3%2A5+%2B+1+
(1) +y+=+16+
and
(2) +y%2Ax+=+80+
(2) +16%2A5+=+80+
(2) +80+=+80+
OK