Solving equations

Question

Find three consecutive odd integers such that the sum of the smallest and half the largest is 10 more than the middle integer

Answer 1

S + L/2 = 10+M

S=x = smallest number

M =x+2 = middle number

L = x+4 = largest number

x + (x+4)/2 = 10+(x+2)

x + x/2 + 2 =10 +x +2

x/2=10

x=20

x+2 = 22

x+4 = 24

20, 22 and 24 are 3 consecutive even integers

where

20+24/2 = 10 + 22

32 = 32

but there are no consecutive odd integers that meet the given relation, just even consecutive integers

5x = 12