The sum of three consecutive numbers is 159

Answer 1

Hi Pyneni!

I'm assuming we need to find 3 consecutive numbers that add to 159.

Another way to think of "consecutive", is that adding 1 to a number will give you the second number. For example, 4 and 5 are consecutive numbers. 4 + 1 = 5

Knowing that, we can pull out 2 equations from your question. Let's call the 3 unknown numbers A, B, and C.

a + b + c = 159

Now, we need to find a second equation. That will give us more information about how the numbers relate to each other. Remember what we talked about consecutive numbers? Since all 3 numbers are consecutive, we can add 1 to the first number to get the second, and add 1 to the second number to get the third. In math terms:

a + 1 = b

b + 1 = c

Do you notice how both equations contain a b term? This means we can combine them for even more information!

(a + 1) + 1 = c

a + 2 = c

Now we have mathematically derived 2 equations for b and c. But we're not done yet, because we need to find the numerical value of the unknown. To do that, we need to use the info we have to rewrite our first equation in terms of one of the variables. Let's choose the variable a to solve for.

a + b + c = 159

Substitute both equations we calculated for b and c

a + (a + 1) + (a + 2) = 159

let's simplify:

3a + 3 = 159

3a = 156

a = 52

Now all the hard work is out of the way since b and c are consecutive!

a + 1 = b

52 + 1 = b

53 = b

a + 2 = c

52 + 2 = c

54 = c

So the 3 consecutive numbers are 52, 53 and 54