The product of two positive integers is 176. one number is 5 more than the other. find the smaller number.

Hello from MrBillDoesMath!

11

Discussion:

Let "n" be the smaller number. Then

n * (n+5) = 176.

My first reaction to this problem was to factor 176 in my head. That's  176 = 16 * 11 and 16 is 5 more than 11. So that's the solution! Now let's solve it using the brute force approach:

n(n+5) = 176                 =>

n^2 + 5n - 176 = 0       => use the quadratic formula

n =     ( -5 +\- sqrt( 5^2 - 4(1)(-176)) )  /2

 =     ( -5 +\- sqrt( 25 +  704) )/ 2

=     ( -5 +\- sqrt (729) ) /2                            => as sqrt(729) = 27

=      (-5 +\- 27) / 2                                        =>

=      (-5 + 27)/2 or ( -5 -27)/2                      =>

=      22/2  or  -32/2                                     =>

=      11 or  -16

But -16 is not allowed as the question wants a positive value.

Thank you,

MrB

answer: slight chance that it will happen

step-by-step explanation:

2x^2+5x+17

your welcome. : )