ratio with sum a sum

Question

what is the ratio between 5 and 3 and a total of 16

Answer 1

Let x and y the two numbers we are looking for. Then, the following system of equation holds:

x/y = 5/3. (first condition)

x+y = 16. (second condition)

Solving the system gives x = 10, y = 6

Answer 2

One way to solve the equations is to take

x/y = 5/3 and multiply both sides by y:

x =5y/3

You can then use substitution to solve for y in the second equation, and finally use the above equation to find x.

NOTE that y cannot be zero if x/y =5/3.