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tickets to college basketball game are $2.50 for students and $3 for general admission. If 174 people attended the last game and the box collected $474, how many each type of ticket did they sell? the box office sold _____ general admission tickets and ______ students tickets.

1 Answer

5 votes

we can write two equations for the statement, and the solve the system

$2.50 for students and $3 for general admission. If 174 people attended the last gam


s+g=174

and the box collected $474


2.50s+3g=474

where s is the number of students and g the number of general admission


\begin{gathered} s+g=174 \\ 2.50s+3g=474 \end{gathered}

to solve the system

we solve a unknow and replace on the other equation ,for example I will solve s from the first equation


\begin{gathered} s+g=174 \\ s=174-g \end{gathered}

now I will replace the value of s on second equation


\begin{gathered} 2.50s+3g=474 \\ 2.50(174-g)+3g=474 \end{gathered}

simplify


\begin{gathered} 2.50*174-2.50g+3g=474 \\ 435+0.50g=474 \\ \end{gathered}

and solve for s


\begin{gathered} 0.50g=474-435 \\ 0.50g=39 \\ g=(39)/(0.50) \\ \\ g=78 \end{gathered}

the value of g (number of general admission) is 78, From this one we can replace the value of g on any equation to solve s

I will replace on the furst equation solved to s


\begin{gathered} s=174-g \\ s=174-78 \\ s=96 \end{gathered}

then the value of s (number of students ) is 96

The box officed sold 78 general admission ticjets and 96 students tickets

User Wong Jia Hau
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