the sum of three consecutive even numbers is 48. what are the three numbers?

Question

anyone know how to help?

Answer 1

Very cute question, Ashley!

This type of question is solved most easily by using a bit of algebra.

We are looking for 3 numbers. We know they consecutive, even numbers, which means they differ by 2. And we're given their sum.

Hence, we can derive an equation to represent this information.

Firstly, let's give the 3 mystery numbers names: a, b, and c.

Next, let's use the information that they are consecutive and even: a, a+2, a+4 [note: b=a+2 and c=a+4]

Next let's use the fact that we also know the sum: a + (a+2) + (a+4) = 48

Which we can simplify: 3a + 6 = 48

=> 3a = 42

=> a = 14

=> b = a+2 = 16 and c = a+4 = 18

So, our three numbers are 14, 16, 18.

As always, a quick check of your answer is suggested: 14+16+18 = 48 (as required). And they are indeed 3 consecutive even numbers.

As an extra note: the sequence a, a+2, a+4 could also be three odd numbers. But we know that in this case they're even numbers because the sum (48) is even. Whereas, if the sum is odd, then they must odd too. What is the sequence of three odd numbers if the sum is 45 instead of 48?

Answer 2

x-1 + x + x+1 = 48

3x = 48

x = 48/3 = 16

15, 16 and 17 are the 3 consecutive numbers adding to 48