Question

Find 3 consecutive odd integers such that 3 times the last number increased by the secondnumber is 50

Answer 1

We want to find three consecutive odd numbers.

Let the first odd number be x.

Then, the second one will be x + 2

The third will be x + 2 + 2, that is, x + 4

3 times the last number increased by the second is 50. That is:

`3(x\text{ + 4) + (x + 2) = 50}`

Solve that by expanding the bracket and collecting like terms:

`\begin{gathered} 3x\text{ + 12 + x + 2 = 50} \\ 3x\text{ + x + 12 + 2 = 50} \\ 4x\text{ + 14 = 50} \\ 4x\text{ = 50 - }14 \\ 4x\text{ = 36} \\ x\text{ = 36/4} \\ x\text{ = 9} \end{gathered}`

Therefore, the three consecutive numbers are:

x = 9

x + 2 = 11

x + 4 = 13

9, 11 and 13