Question

The sum of two numbers is 150. The ratio of the same two numbers is 3:2. Find the bigger number. Please show work and explain. (:

Answer 1

x, y - the numbers

The sum of two numbers is 150.

`x+y=150 \ \ \ |-y \\ x=150-y`

The ratio of the two numbers is 3:2.

`(x)/(y)=(3)/(2) \ \ \ |* y \\ x=(3)/(2)y`

Set both expressions equal to each other:

`x=x \\ 150-y=(3)/(2)y \ \ \ |+y \\ 150=(3)/(2)y+y \\ 150=(3)/(2)y+(2)/(2)y \\ 150=(5)/(2)y \ \ \ |* (2)/(5) \\ 150 * (2)/(5)=y \\ 30 * 2=y \\ y=60 \\ \\ x=150-y=150-60=90`

The numbers are 60 and 90.
The bigger number is 90.