Question

The ratio of two numbers is 5 to 4 and the sum of the numbers is 63. What are the numbers?

Answer 1

35 and 28.

Explanation:

This problem can be solved using a system of linear equations.

Let one number be x and the other be y.

"The ratio of two numbers is 5 to 4", therefore:

`(x)/(y) =(5)/(4) \\\\(x)/(y) =1.25`

Also, "...the sum of the numbers is 63", therefore:

`x+y=63`

1. Set up the linear equations system.

`(x)/(y) =1.25\\\\x+y=63`

2. Take the value of one of the variables from one of the equations.

`(x)/(y) =1.25\\x=1.25y`

3. Substitute this value into the other equation and solve for y.

`x+y=63\\\\(1.25y)+y=63\\\\2.25y=63\\\\y=(63)/(2.25) \\\\y=28`

4. Now that we have a value for y, take an equation and find the value of x.

`x+y=63\\\\x+(28)=63\\\\x=63-28\\\\x=35`

Therefore, our 2 numbers are 35 and 28.