SOLUTION: The product of Hanny's and younger brother Robert's ages is 135. When their ages are divided, the quotient is 1 and the remainder is 6. How old are they now?

Question 958974: The product of Hanny's and younger brother Robert's ages is 135. When their ages are divided, the quotient is 1 and the remainder is 6. How old are they now?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
let h = hanny's age.
let r = robert's age.
h*r = 135
h/r = 1 + remainder of 6.

you could use trial and error and you would get the following:

135 has to be divisible by 5 because the factors have to be integers.

this is not really stated, but i think it's implied.

whether this assumption is valid or not, it does lead to an answer that is corroborated by the more advanced solution to come later.

looking for the two factors that, when multiplied together, equal 135 yields the following.

135/5 = 27, so 5 * 27 = 135 but 27/5 doesn't have a quotient of 1, so these factors don't work.

135 / 10 = 13.5, so 13.5 * 10 = 135, and 13.5 / 10 give you a quotient of 1 but not a remainder of 6, these factors don't work..

135 / 15 = 9, so 15 * 9 = 135, and 15/9 = 1 with a remainder of 6, so this looks like the one.

hanny is 15 and roberto is 9 looks like your solution.

now for the more advanced way to solve it.

you have h * r = 135

you also have h / r = 1 + remainder of 6, which can also be shown as:

h/r = 1 + (6/r)

you have:

h*r = 135
h/r = 1 + (6/r)

in the second equation of h/r = 1 + (6/r), solve for h to get:

h = (1 + 6/r) * r which simplifies to:

h = (r + 6)

in the first equation of h*r = 135, replace h with (r + 6) to get:

(r + 6)*r = 135

simplify to get:

r^2 + 6r = 135

subtract 135 from both sides of the equation to get:

r^2 + 6r - 135 = 0

factor this equation to get:

(r + 15) * (r - 9) = 0

solve for r to get:

r = -15 or r = 9

r can't be negative, so r must be equal to 9.

the original equation of h*r = 135 can now be solved for h.

this results in h = 15.

the solution is h = 15 and r = 9.

both methods get the same solution so it looks good.

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