# Number Problem 20

### From Homeworkwiki

**Find two numbers such that their difference, sum and product are to one another as 1 : 7 : 24.**

**Solution:** Let the numbers be x and y

We have (x - y) : (x + y) : xy = 1 : 7 : 24

(x - y) : 1 = (x + y) : 7 = xy : 24

7(x - y) = x + y

6x = 8y

x = 8y/6 = 4y/3

x - y = xy / 24

4y/3 - y = 4y/3 X y/24

y/3 = 4y^{2} / 72

i.e. 24y = 4y^{2}

i.e. y^{2} - 6y = 0

y = 0 or 6

x = 4/3 x 6 = 8

Hence, the numbers are 6 and 8