Mathematics
wglenda26
2

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?

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(1) Answers
katiebabyyy

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... [latex]\#kids=4.5*x[/latex] [latex]\#adults=8.5*y[/latex] we know that all group are formed by kids and adults, so... [latex]4.5*x+8.5*y=79[/latex] now we need more one equation, but we can see... "There were 6 fewer adults than kids in the group." translating... [latex]y=x-6[/latex] then... [latex]\begin{Bmatrix}4.5*x+8.5*y&=&79\\y&=&x-6\end{matrix}[/latex] now we can replace the second row at first row [latex]\begin{Bmatrix}4.5*x+8.5*(x-6)&=&79\\y&=&x-6\end{matrix}[/latex] [latex]\begin{Bmatrix}4.5*x+8.5*x-51&=&79\\y&=&x-6\end{matrix}[/latex] [latex]\begin{Bmatrix}4.5*x+8.5*x&=&79+51\\y&=&x-6\end{matrix}[/latex] [latex]\begin{Bmatrix}13*x&=&130\\y&=&x-6\end{matrix}[/latex] [latex]\begin{Bmatrix}x&=&10\\y&=&x-6\end{matrix}[/latex] now we replace the value that we found... [latex]\begin{Bmatrix}x&=&10\\y&=&10-6\end{matrix}[/latex] [latex]\boxed{\boxed{\begin{Bmatrix}kids&=&10\\adults&=&4\end{matrix}}}[/latex]

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