Question

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.

Answer 1

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

$\begin{gathered} 2.50\times174-2.50g+3g=474 \\ 435+0.50g=474 \\ \end{gathered}$

and solve for s

$\begin{gathered} 0.50g=474-435 \\ 0.50g=39 \\ g=\frac{39}{0.50} \\ \\ g=78 \end{gathered}$

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