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# Consecutive Numbers

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

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.

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

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