The Product of Two Consecutive Positive Integers is 55 More Than Their Sum


Question: The product of two consecutive positive integers is 55 more than their sum. Find the integers.

An integer is positive if it is greater than zero.

Answer: The consecutive integers whose product is 55 more than their sum are 8 and 9.

Let's change the given statemetn into the equation and find the integers.

Explanation:

Let the two consecutive integers be x and (x + 1)

Sum of the integers = x + (x + 1) = 2x + 1

Product of the integers = x(x +1)

According to the question,

Product of the integers = Sum of the integers + 55

x(x + 1) = 2x + 1 + 55

x2 + x = 2x + 56

x2 + x - 2x  = 56

x2 - x - 56 = 0

x2 - 8x + 7x - 56 = 0

(x - 8)(x + 7) = 0

Thus, x = 8 and x = -7

Since, the integers have to be positive consecutive integers we neglect x = -7

Thus, x = 8

Verification:

If x = 8 then, x + 1 = 9

8 × 9 = 72

8 + 9 + 55 = 72

Thus, the consecutive integers whose product is 55 more than their sum are 8 and 9.