Question

The sum of 5 times one number, x, and 4 times a second number, y, is 75. If the sum of the two numbers is 18, find the two numbers.

Enter a system of equations to represent the situation, then solve the system.

Answer 1

Answer:
`x=3` and
`y=15`

Explanation:

First, we are told "sum of 5 times one number, x, and 4 times a second number, y, is 75":

`5x+4y=75` (1)

Then, we are told "he sum of the two numbers is 18":

`x+y=18` (2)

At this point we have our system of equations and now we are able to find the values of
`x` and
`y`.

So, let's begin by isolating
`x` from (2):

`x=18-y` (3)

Substituting (3) in (1):

`5(18-y)+4y=75` (4)

Finding
`y`:

`90-5y+4y=75`

`y=15` (5) This is the value of
`y`

Substituting (5) in (1):

`5x+4(15)=75` (6)

Finding
`y`:

`5x+60=75` (7)

`x=3` (8) This is the value of
`x`