SOLUTION: Josh and Sam have ages that are consecutive odd integers.The product of their ages is 575.How old is Josh if he is the younger brother?Solve algebraically

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Question 961513: Josh and Sam have ages that are consecutive odd integers.The product of their ages is 575.How old is Josh if he is the younger brother?Solve algebraically

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +n+ and +n%2B2+ = their ages
which are consecutive odd integers
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+n%2A%28+n%2B2+%29+=+575+
+n%5E2+%2B+2n+=+575+
Complete the square
+n%5E2+%2B+2n+%2B+%282%2F2%29%5E2+=+575+%2B+%282%2F2%29%5E2+
+n%5E2+%2B+2n+%2B+1+=+576+
+%28+n+%2B+1+%29%5E2+=+24%5E2+
+n+%2B+1+=+24+
+n+=+23+
+n%2B2++=+25+
Their ages are 23 and 25
check:
+23%2A25+=+575+
+575+=+575+