x - y = 13
-y=-x + 13
y = x-13
Let bigger number be x
smaller number x - 13
ratio of the two: x/x-13
quotient = 2 × 5/x-13
= 2 (x-13)+5
x-13
= 2x - 21
x-13
Equation:
x = 2x - 21
x-13 x - 13
2x - x = 21
x-13 x-13
x (x-13) = 21 (x-13)
x-13 x-13
x = 21
The numbers are:
Bigger number, x = 21
smaller number, x-13 = 21-13 = 8
The numbers are 21 and 8.
To Check:
21-8 = 13
21/8 = 2 and 5/8