Question

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

Answer 1

11

Explanation:

let x be the smaller number.

from question statement,we get

x(x+5)=176

x²+5x=176

adding -176 in both sides of equation,we get

x²+5x-176=176-176

x²+5x-176=0

by factorization, split the middle term to make the equation into such that the sum of two numbers should be 5 and their product be -176.

x²+16x-11x-176=0

Making two groups and taking the common out:

x(x+16)-11(x+16)=0

(x+16)(x-11)=0

either x+16=0 or x-11=0

either x=-16 or x=11.

-16 is not positive. so, 11 is the smaller number.

Answer 2

Hello from MrBillDoesMath!

Answer:

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