Question

1. Find 3 consecutive integers whose sum is 33.

Answer 1

Answer:

  10, 11, 12

Step-by-step explanation:

For problems involving consecutive integers, I like to consider their average value. For three consecutive integers, their average will be the middle one. It will be ...

  average = sum / (number of numbers) = 33/3 = 11

The middle number is 11, so the numbers are ...

  10, 11, 12

_____

If you want to write an equation, you can let x represent the middle number. Then the other two are x-1 and x+1, and their sum is ...

  (x-1) +(x) +(x+1) = 33 = 3x

  x = 11   ⇒   x-1 = 10, x+1 = 12

Answer 2

Answer: 10, 11, 12

Step-by-step explanation: Think of the integers like this:

1st integer: x

2nd integer: x+1

3rd integer: x+2

That is necessary because they are consecutive integers. Since the sum is 33, we need to create an equation.

x+x+1+x+2=33.

Simplify:

3x+3=33.

Opposite operations:

3x=-3+33.

To get the 3 close to the 33, we needed to make it negative, which is the opposite operation of the positive 3.

So,

3x=30.

Divide by 3:

x=10.

The first integer, x, equals 10.

To go with the guide that we already created,

1st integer: x=10

2nd integer: x+1=11

3rd integer:x+2=12.

Therefore, the three consecutive integers are 10, 11, and 12.

To check that, add them up. They all equal 33 and they are consecutive, which means this is the right answer!