When you add three consecutive odd integers together, the sum equals 117. What are the three integers?

Answer 1

Answer 2

Way 1: Set up 3 odd terms below

Step 1: write what's given

n+1, n+3, n+5

Make sure you guess and check your findings when you are done.

find the three terms given sum is 117

Step 2: Set up an equation

(n+1)+(n+3)+(n+5)=117

Step 3: Solve for n

3n+9=117

Step 4: Divide by n

3n=108

n=108/3=36

Step 5, subsitute n=36 to n+1,n+3,n+5

Three consecutive integers is 37,39, 41.

Step 6: Guess and check if solutions match up to the sum

37+39+41=117 so it's confirmed.

Way 2:

Step 1:

Let n, be a number, n+2, n+4 are incrementing terms for the consecutive odd integers.

set 3 terms equal to 117

Step 2: set up equation

n+n+2+n+4=117

Step 3: Solve for n

3n=111

n=37

Answers will be same as the other way.

Answer 3

Answer 4

Let’s say the first integer is x. The second integer would then be x+2, then x+4 for the 3rd integer.

This is because consecutive odd numbers would be every other consecutive number. Instead of just adding 1 to the previous number, you would have to add 2.

Sum means to add, so we have x+(x+2)+(x+4).

Is means equal, so we have x+(x+2)+(x+4)=117.

For addition we can drop the parenthesis and combine like terms:

x+x+2+x+4=117

3x+6=117

The subtract 6 from both sides to get 3x=111.

The divide both sides by 3 to get x=37.

37 is the first of the 3 consecutive odd integers.

Substitute 37 into x+2 and x+4 to get 39 and 41 respectively.

The 3 consecutive odd integers that add to 117 are 37, 39, and 41

Answer 5

Say that we have 3 consecutive odd numbers that add to 117, and that x is the smallest of these numbers. The next odd number after x would be x + 2, and then x + 4 after that. So, even though we don't know the exact value of x, we know that

x + (x + 2) + (x + 4) = 117,

where x is the smallest of three consecutive odd numbers. Combining like terms and simplifying, we have

(x+x+x) + (2+4) = 117

3x + 6 = 117

3x = 111

x = 37.

This implies x + 2 = 39 and x + 4 = 41, and hence {37, 39, 41} are three consecutive odd numbers that sum to 117.

Answer 6

Hello!

It's helpful to set up the equation with the information that we know. There are 3 integers whose sum will equal 117, so we can represent that as:

a + b + c = 117

Since the odd integers are consecutive, we can set those equations up as follows:

b = a + 2

c = a + 4

We can plug the new expressions back into the original equation so that we can solve for a:

a + a + 2 + a + 4 = 117

3a + 6 = 117

3a = 111

a = 37

b = 37 + 2 = 39

c = 37 + 4 = 41

As a check, we can add 37 + 39 + 41 to ensure that we get 117 and these 3 numbers added together equals 117.

Answer 7

If you posit x as the first number of the sequence, you have:

x + (x + 2) + (x + 4) = 117

The addition of 2 and 4 is so that we have the consecutive odd numbers after x.

It is then a matter of solving the equation:

3x + 6 = 117

3x = 111

x = 37

So the answer is 37, 39, 41.