Chapter 6.4, Problem 8P

Solve each word problem

At an all-you-can-eat barbeque fundraiser that you are sponsoring, adults pay $6 for a dinner and children pay $4$ for a dinner. 212 people attend and you raise $1128. What is the total number of adults and the total number of children attending?

a. What is a system of equations that you can use to solve this problem?

b. What method would you use to solve the system? Why?

To determine

To determine the total number of adults and the total number of children attending the dinner. Write the system of equation and name of the method used to solve them.

Answer to Problem 8P

Number of adults: 140, Number of children: 72,

System of equation: $\begin{array}{l}x+y=212\\ 6x+4y=1128\end{array}$

Method used to solve the system of equations: Elimination method

Explanation of Solution

Given: A barbeque fundraiser is sponsored where adults pay &6 for a dinner and children pay $4 for a dinner. 212 people attend it and the money raised was $1128.

Calculation:

Let the number of adults attending the dinner is x and number of children is y . So money collected from all adults is 6x and that from children is 4y . Total money collected is 6x+4y.

Now the system of equations,

  $x+y=212$



  $6x+4y=1128$



Multiply equation 1.1 by 4 and subtract from equation 1.2,

  $\begin{array}{l}\left(6x+4y\right)-\left(4x+4y\right)=1128-848\\ \Rightarrow 6x-4x=280\\ \Rightarrow 2x=280\\ \Rightarrow x=\frac{280}{2}\\ \Rightarrow x=140\\ \Rightarrow y=212-140=72\end{array}$

Hence, the number of adults is 140 and that of children is 72.Method used to solve the system of equation is elimination method.