Write an equation and solve

Question

Find three consecutive odd integers whose sum is 63

Answer 1

When you're working with more than two consecutive things (integers, odd numbers, whatever), sometimes it's easiest to let x be the middle one, instead of the first one.

Since we want three consecutive odd integers, we let the middle odd number be x.

The odd number just before x is: x - 2.

The odd number just after x is: x + 2.

We want the sum of these numbers to be 63, so

(x - 2) + x + (x + 2) = 63.

Simplify the left hand side and then divide both sides by 3:

3x = 63

x = 21

Notice that 21 is odd. That's good, because we're looking for odd numbers!

Since 21 is the second of the three consecutive odd numbers, all three numbers are 19, 21, and 23. (We're asked for all three integers, so we can't stop with just the value of x.)

It's a good idea to check our work: 19 + 21 + 23 does indeed equal 63.

Answer 2

Here is different way sort of to arrive at same answer

first number must be odd, N₁=2x+1 ,,,,x any positive integer or zero

N₁ now is odd for sure

N₂=2x+3

N₃=2x+5

adding and equating to 63

6x+9=63

x=9

2x+1=19

Answer 3

Hi Gift P

19, 21 and 23

Let x = an odd number

Then x + 2 and x + 4 will also be odd numbers because an even integer plus and odd integer is always an odd integer. You can look up the reasons and or proofs of this in your text or online.

So (x + 2) and (x + 4) will be the next two consecutive odd integers

x + (x+2) + (x+4)=63

Combine’

x + x + 2 + x + 4 = 63

3x + 6 = 63

3x = 63 -6

3x = 57

x = 57/3

x = 19

x + 2 = 21

x + 4 = 23

Checking

19 + 21 + 23 = 63

40 + 23 = 63

63 = 63

I hope this helps. You can check out: The sum of an even and odd integer is of the form 2n+2m+1=2(n+m)+1 so it is odd., in your text or online