Question

The difference between two numbers is 16. Five times the smaller is the same as 8 less than twice the larger. Find the numbers

Answer 1

`x,y-\text{the numbers},~x>y\\\\ x-y=16\\ 5y=2x-8\\\\ x=16+y\\ 5y=2x-8\\\\ 5y=2(16+y)-8\\ 5y=32+2y-8\\ 3y=24\\ y=8\\\\ x-8=16\\ x=24\\\\ \boxed{x=24,y=8}`

Answer 2

x - the larger number
y - the smaller number

The difference between two numbers is 16.

`x-y=16 \\ x=16+y`

Five times the smaller is the same as 8 less than twice the larger.

`5y=2x-8 \\ 5y+8=2x \\ (5)/(2)y+4=x \\ \\ x=x \\ 16+y=(5)/(2)y+4 \\ y-(5)/(2)y=4-16 \\ (2)/(2)y-(5)/(2)y=-12 \\ -(3)/(2)y=-12 \\ y=-12 * (-(2)/(3)) \\ y=4 * 2 \\ y=8 \\ \\ x=16+y=16+8=24`

The numbers are 24 and 8.