At an all-you-can-eat barbequefundraiser 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?
+26367 At an all-you-can-eat barbequefundraiser 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?
\(\text{Let number of adults $=a$} \\ \text{Let number of children $=c$}\)
\(\begin{array}{|rcll|} \hline a+c &=& 212 \\ \mathbf{c} &=& \mathbf{212-a} \\ \hline \end{array}\)
\(\begin{array}{|rcll|} \hline 6a+4c &=& 1128 \\ 6a +4(212-a) &=& 1128 \\ 6a + 4*212-4a &=& 1128 \\ 6a + 848-4a &=& 1128 \\ 2a &=& 1128-848 \\ 2a &=& 280 \quad | \quad : 2 \\ \mathbf{a} &=& \mathbf{140} \\\\ \mathbf{c} &=& \mathbf{212-a} \\ c &=& 212-140 \\ \mathbf{c} &=& \mathbf{72} \\ \hline \end{array}\)
The total number of adults is 140
The total number of children is 72
