If three consecutive even numbers are added together the result is 42. find the smallest number.

What three consecutive integers have a sum of 42?

Here we will use algebra to find three consecutive integers whose sum is 42. We start by assigning X to the first integer. Since they are consecutive, it means that the 2nd number will be X + 1 and the 3rd number will be X + 2 and they should all add up to 42. Therefore, you can write the equation as follows: (X) + (X + 1) + (X + 2) = 42 To solve for X, you first add the integers together and the X variables together. Then you subtract three from each side, followed by dividing by 3 on each side. Here is the work to show our math: X + X + 1 + X + 2 = 42

3X + 3 = 42

3X + 3 - 3 = 42 - 3

3X = 39

3X/3 = 39/3

X = 13

Which means that the first number is 13, the second number is 13 + 1 and the third number is 13 + 2. Therefore, three consecutive integers that add up to 42 are 13, 14, and 15.

13 + 14 + 15 = 42

We know our answer is correct because 13 + 14 + 15 equals 42 as displayed above.
Three Consecutive Integers Enter another number below to find what three consecutive integers add up to its sum.

What three consecutive integers have a sum of 43?

Here is the next algebra problem we solved.
Copyright  |   Privacy Policy  |   Disclaimer  |   Contact

(a) 12, 13 and 14.

(b) 12, 14 and 16.

(c) 13, 14 and 15.

(d) 13, 15 and 17

(b)

Explanation:

          Let the smallest even whole number = x,

          Therefore, the next even whole number = (x + 2)

          And the third even whole number = x + 2 + 2 = x + 4

          Now, x + (x + 2) + (x + 4) = 42

         

 3x + 6 = 42  x = 12

          Therefore numbers are 12, 14 and 16.

1 Expert Answer

We can call the lowest integer x, the next integer x+2 (since our integers need to be even) and the third integer x+4. Now we can set up an algebraic equation. 42=x+(x+2)+(x+4).

Combine like terms on the right side,

Subtract 6 from each side

x=12, which is our lowest integer. 

The next two integers we find with 12+2=14 and 12+4=16. Or just simply take the next two even integers. Thus, 12+14+16=42.