The sum of two numbers is 640. If you divide the bigger number by the smaller, you'll get quotient 7 and remainder 64. Find the numbers.

let 'x' and 'y' represent the two numbers and x>y

The sum of two numbers is 640:

x + y = 640

If you divide the bigger number by the smaller, you’ll get quotient 7 and remainder 64:

x = 7y + 64

by solving the system of equations:

x + y = 640

x = 7y + 64

we find:

x = 568

y = 72

let b>a

a+b=640, a=640-b

b/a=7+64/a, using a from above this becomes:

b / (640-b) = 7+64 / (640-b)

b / (640-b) = (4480-7b+64) / (640-b)

b=4544-7b

8b=4544

b=568, and since a=640-b:

a=72

so the two number are 72 and 568

check ...

72+568=640

640=640

...

568/72=7+64/72

568/72 = (504+64) / 72

568/72=568/72