Twice the sum of 3 consecutive integers is 18. What is the quotient of the largest integer and the smallest integer?

Question

  make an outline and a equation

Answer 1

Let x = the first integer

Let y = the second integer

Let z = the third integer

 

First, we know that the numbers are consecutive. This means the following:

 

y = x + 1

z = y + 1 = x + 2

 

Second, we are given that twice the sum of all 3 numbers is 18. This means the following:

 

2 * (x + y + z) = 18

x + y + z = 9

 

Since we have y and z both in terms of x, we can substitute them into this equation:

 

x + (x + 1) + (x + 2) = 9

x + x + x + 3 = 9

3x = 6

x = 2

 

Therefore, x = 2, y = 3, z = 4.

 

We are asked for the quotient of the largest integer and the smallest integer. This means what is z / x?

 

z = 4, x = 2. Therefore the quotient is 4/2 = 2.

Answer 2

The three numbers are:

 

n

n + 1

n + 2

 

From the given information,

 

2[n + (n + 1) + (n + 2)] = 18

 

2(3n + 3) = 18

 

6(n + 1) = 18

 

n + 1 = 3

 

n = 2

 

(n + 2) / n = (2 + 2) / 2 = 2

 

Quotient of the largest integer and the smallest integer is 2.