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Question: There are three consecutive positive integers. The product of the first two integers is 2 more than 9 times the third integer. Find the integers.


A ) 9, 10, 11
B ) 10, 11, 12
C ) 6, 7, 8
D ) 2, 3, 4

Steps to derive

1 1st integer × 2nd integer = 2 + (9 × 3rd integer) .

2 Let the first integer be x.

3 Then 2nd integer = x + 1 and 3nd integer = x + 2.

4 x(x + 1) = 2 + 9(x + 2)

5 x2 + x = 2 + 9x + 18
 [Distributive property.]

6 x2 - 8x - 20 = 0
 [Simplify.]

7 (x - 10)(x + 2) = 0

8 x = 10 or x = - 2

9 The integers are positive. So, x = 10.

10 The consecutive integers are 10, 11, 12.



Hence the right answer is Option B

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