wglenda26
9

A group of adults and kids went to see a movie. Tickets cost $8.50 each for adults and$4.50 each for kids, and the group paid \$79.00 in total. There were 6 fewer adults than kids in the group. I'm new to this kind of problem and I don't understand how to do this. How do I find what this is asking for? Can someone go through it step-by-step for me please?

I'm sorry about my bad english, but I'll try to help you, OK?! first we need to attribute a name to the variable, let's call each number means the price... $\#kids=4.5*x$ $\#adults=8.5*y$ we know that all group are formed by kids and adults, so... $4.5*x+8.5*y=79$ now we need more one equation, but we can see... "There were 6 fewer adults than kids in the group." translating... $y=x-6$ then... $\begin{Bmatrix}4.5*x+8.5*y&=&79\\y&=&x-6\end{matrix}$ now we can replace the second row at first row $\begin{Bmatrix}4.5*x+8.5*(x-6)&=&79\\y&=&x-6\end{matrix}$ $\begin{Bmatrix}4.5*x+8.5*x-51&=&79\\y&=&x-6\end{matrix}$ $\begin{Bmatrix}4.5*x+8.5*x&=&79+51\\y&=&x-6\end{matrix}$ $\begin{Bmatrix}13*x&=&130\\y&=&x-6\end{matrix}$ $\begin{Bmatrix}x&=&10\\y&=&x-6\end{matrix}$ now we replace the value that we found... $\begin{Bmatrix}x&=&10\\y&=&10-6\end{matrix}$ $\boxed{\boxed{\begin{Bmatrix}kids&=&10\\adults&=&4\end{matrix}}}$