Question

The product of the second and third of three consecutive integers is 2 more than 15 times the first integer. Find the integers.

Select the correct choice below and fill in the answer box(es) to complete your choice. (Use a comma to separate answers as needed.)

A. There is only one solution. The only three consecutive integers are ______.

B. There are two solutions. The three smaller consecutive integers are ______ or the three larger consecutive integers are ________.

Answer 1

Answer:

Option B.

There are two solutions. The three smaller consecutive integers are 0,1,2 or the three larger consecutive integers are 12,13,14

Step-by-step explanation:

Let

x ----> the first consecutive integer

x+1 ---> the second consecutive integer

x+2 --> the third consecutive integer

we have that

The product of the second and third of three consecutive integers is 2 more than 15 times the first integer

so

The linear equation that represent this situation is

$(x+1)(x+2)=15x+2$

solve for x

$x^2+2x+x+2=15x+2\\x^2+3x+2=15x+2\\x^2-12x=0\\x(x-12)=0$

so

the solutions for x are

x=0 and x=12

For x=0

The second and third consecutive integer are 1 and 2

For x=12

The second and third consecutive integer are 13 and 14

therefore

There are two solutions. The three smaller consecutive integers are 0,1,2 or the three larger consecutive integers are 12,13,14