Consecutive Numbers

Question

When you subtract the third of three consecutive odd integers from 4times the first, the difference is 29. What are the three numbers.

Answer 1

Hello, Dustin. Let's assign variables for the three consecutive odd numbers: x, x+2, and x+4. The first odd number is x, the second is 2 greater than x, and the third is 4 greater than x.

Now let's create an equation. 4x-(x+4)=29. In words, 4 times the first consecutive odd number, which is x, minus the third consecutive odd number, which is x+4, equals 29.

Now let's solve the equation.

4x-(x+4)=29  (First you have to add the third consecutive odd number to both sides of the equation.)

4x= 29 + x + 4  (Add 29 + 4.)

4x= 33 + x  (Now subtract x from both sides of the equation.)

3x=33  (Divide both sides of the equation by 3.)

x=11, x+2=13, x+4=15

The three consecutive numbers are 11, 13, and 15.

Hope this helps, Dustin.

Answer 2

The odd integer formula is 2n - 1, but because you have two more consecutive odd numbers you have to add in a "+2" to each so that

odd integer 1 = 2n - 1

odd integer 2 = 2n -1  + 2

odd integer 3 = 2n -1 + 2 + 2

All that remains is to construct the equation using the information given, specifically that the difference of 4 times the integer 1 and integer 3 is equal to 29

4(2n-1) - (2n+3) = 29

8n - 4 - 2n - 3 = 29

6n = 36

n = 6

Now you have to use the factors from the original equation to get the actual iintegers

2n - 1 = 11

2n + 1 = 13

2n + 3 = 15

Use those values to check and:

4*11 - 15 = 29

44 - 15 = 29

29 = 29