Question

A box contains orange balls and green balls. The number of green balls is eight more than four times the number of orange balls. If there are 123 balls altogether, then how many green balls and how many orange balls are there in the box?

Answer 1

Let "x" be the number of orange balls and let "y" be the number of green balls.

We know that the number of green balls is eight more than four times the number of orange balls. So, we can write this as:

`y=4x+8`

And, we also know that there are 123 balls altogether. So,

`x+y=123`

We're going to solve the system:

`\begin{gathered} y=4x+8 \\ x+y=123 \end{gathered}`

Notice that we could replace the first equation in the second one:

`\begin{gathered} x+y=123 \\ x+(4x+8)=123 \\ 5x+8=123 \\ 5x=123-8 \\ 5x=115 \\ x=(115)/(5)=23 \end{gathered}`

Then, there are 23 orange balls.

To find the number of green balls, we replace x=23 in any of both equations of the system:

`\begin{gathered} x+y=123 \\ 23+y=123 \\ y=123-23 \\ y=100 \end{gathered}`

Therefore, there are 100 green balls