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Blank High School sells Prom tickets for $75 per couple and $50 per single. If a total of 173 students attended the prom and blank High School earned $7050. How many of each type of ticket did blank High School sell.

User Bjarte
by
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1 Answer

2 votes

Let x be the number of couple tickets and let y be the number of single tickets sold.

We know that the school earned a total of $7050, then we have that:


75x+50y=7050

Now, we also know that the total number of students was 173, then we have:


2x+y=173

Hence we have the system of equations:


\begin{gathered} 75x+50y=7050 \\ 2x+y=173 \end{gathered}

To solve this system we multiply the second equation by -50, then we have:


\begin{gathered} 75x+50y=7050 \\ -100x-50y=-8650 \end{gathered}

Adding this equation we have:


\begin{gathered} -25x=-1600 \\ x=(-1600)/(-25) \\ x=64 \end{gathered}

Once we know the value of x we plug it in the second equation to get y:


\begin{gathered} 2(64)+y=173 \\ y=173-128 \\ y=45 \end{gathered}

Therefore, they sold 64 couple tickets and 45 single tickets.

User Gilsdav
by
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