SOLUTION: danny is 7 years older than his brother. If the product of their ages is 120, find their ages. I have tried the equation n(n+7)=120. This does not make sense, however, since

Question 623550: danny is 7 years older than his brother. If the product of their ages is 120, find their ages. I have tried the equation n(n+7)=120. This does not make sense, however, since 7 does not divide into 120 evenly.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
danny is 15
his brother is 8
the difference in their ages is 15 - 8 = 7.
the product of their ages is 15 * 8 = 10 * 8 + 5 * 8 = 80 + 40 = 120
you had the right formula.
you just didn't know how to work it.
here's how:
let n equal danny's brother's age.
this make danny's age equal to n + 7.
this make the product of their ages equal n(n+7).
you are given that the product of their ages is 120, so:
n(n+7) = 120
simplify this expression to get:
n^2 + 7n = 120
subtract 120 from both sides of the equation to get:
n^2 + 7n - 120 = 0
factor to get:
(n+15)(n-8) = 0
solve for n to geet:
n = -15 or n = 8
-15 is no good because it's negative.
answer is that n = 8.
that's danny's brother's age.
danny is 7 more than that so danny is 15.
what you had was a quadratic equation that could be solved.

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