The ratio of three numbers is 2:3:4. The largest number is 10 more than the smallest. What is the middle number?

Let's say the smallest number is x, then the largest number is 10+x. Now we can let y be the factor that we multiply the ratio by to get the original numbers. So we have xy=2 and 10y+xy=4. Subtracting the 1st equation from the 2nd we get 10y=2 so y=1/5 which means x=10 and 10+x=20 so the middle number is 15.