Question

Find two positive numbers if their ratio is 8:5 and the difference is 150.

Answer 1

Let's call the two numbers x and y. We can write a system of equations to describe the situation:

5x = 8y

x - y = 150

Let's solve the first equation for x:

x = 8y/5

Now we can use substitution to solve the system by plugging 8y/5 in for x in the second equation:

(8y/5) - y = 150

Simplify:

3y/5 = 150

3y = 750

y = 250

If y = 250, then x is:

x = 8(250)/5 = 400

The answer is 250 and 400.