Question

I need help with Systems of 2 equations Word Problems. Could some one help?

Answer 1

Let x be the number of children and let y be the number of adults.

We know that the total number of attendants was 147, then:

`x+y=147`

We also know that each child ticket cost $4 and for each adult cost $12, and the total amount collected were $1156. Then we have:

`4x+12y=1156`

Hence we have the system:

`\begin{gathered} x+y=147 \\ 4x+12y=1156 \end{gathered}`

Now we have to solve the system. To do that we solve the first equation for y:

`y=147-x`

and we plug this value into the second equation and solve for x:

`\begin{gathered} 4x+12(147-x)=1156 \\ 4x+1764-12x=1156 \\ -8x=1156-1764 \\ -8x=-608 \\ x=(-608)/(-8) \\ x=76 \end{gathered}`

Now that we have the value we can find the value of y, then:

`\begin{gathered} y=147-76 \\ y=71 \end{gathered}`

Therefore there were 76 children and 71 adults.