SOLUTION: Ben is four years older than josh. the product of their ages is 437. how old are they both?

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Question 939861: Ben is four years older than josh.
the product of their ages is 437.
how old are they both?
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

let Ben's age be B and Josh's age J
if Ben is four years older than Josh, then we have
B=J%2B4.....eq.1
if the product of their ages is 437, then we have

B%2AJ=437.....eq.2 ....substitute J%2B4 for B from eq.1
%28J%2B4%29%2AJ=437.....solve for J
J%5E2%2B4J=437
J%5E2%2B4J-437=0...use quadratic formula
J+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
J+=+%28-4+%2B-+sqrt%28+4%5E2-4%2A1%2A%28-437%29+%29%29%2F%282%2A1%29+
J+=+%28-4+%2B-+sqrt%28+16%2B1748+%29%29%2F2+
J+=+%28-4+%2B-+sqrt%28+1764+%29%29%2F2+
J+=+%28-4+%2B-+42%29%2F2+

solution: we will nee only positive solution since age cannot be negative
J+=+%28-4+%2B+42%29%2F2+
J+=+38%2F2+
highlight%28J+=+19%29+
now find Ben's age:
B=J%2B4.....eq.1
B=19%2B4
highlight%28B=23%29