What is the smallest number for three consecutive even integers whose sum is 28?

3 Answers
Jan 30, 2018

See a solution process below:

Explanation:

First, let's call the smallest number n

Then, because they are consecutive even numbers we can add 2 and 4 to n to name the other two numbers:

  • n + 2

  • + 4

Now, we can write this equation and solve for n:

n + (n + 2) + (n + 4) = 90

n + n + 2 + n + 4 = 90

n + n + n +2 + 4 = 90

1n + 1n + 1n + 6 = 90

(1 + 1 + 1)n + 6 = 90

3n + 6 = 90

3n + 6 - color(red)(6) = 90 - color(red)(6)

3n + 0 = 84

3n = 84

(3n)/color(red)(3) = 84/color(red)(3)

(color(red)(cancel(color(black)(3)))n)/cancel(color(red)(3)) = 28

n = 28

The smallest of the three numbers is 28

Jan 30, 2018

The smallest number is 28

Explanation:

Let n = the smallest number
Let n+2 = the second consecutive number
Let n+4 = the third consecutive number

So the equation will be

n + n+2 + n + 4 = 90 Combining like terms gives.

3n + 6 = 90 subtract 6 from both sides

3n + 6 -6= 90 -6-6 This gives

3n =84 divide both sides by 3

(3n)/3 = 84/3 This gives

n =28

Jan 30, 2018

The smallest of the three consecutive even numbers with a sum of 90 is 28.

Explanation:

We should first put this word problem into an algebraic equation to make it easier to solve.

Let n be the lowest of the three consecutive even numbers.

We know that our three consecutive even numbers must therefore be color(red)(n), color(red)(n + 2), and color(red)(n + 4). We also know what their sum should be.

color(red)(n) + color(red)(n + 2) + color(red)(n + 4) = color(green)(90)

Now, we can solve for n as usual.

3n + 6 = 90

3n = 84

color(blue)(n = 28)

And double-checking with this as our lowest of the three consecutive even-numbers:

color(blue)(28) + color(blue)(28) color(red)(+ 2)+ color(blue)(28) color(red)( + 4)

= color(green)(90)