Question

Admission to a baseball game is $2.00 for general admission and $6.50 for reserved seats .The receipts were $3331.50 for 930 paid admissions. How many of each ticket were sold?( round to the nearest intergar if necessary.)

Answer 1

we can write a equation for each statement

The receipts were $3331.50

`2g+6.50r=3331.50`

where g is the number of general ticket and r the number of reserverd ticket

930 paid admissions

`g+r=930`

we have two equations, we can solve a variable for the second equation an replace on the firts, i will solve g

`g=930-r`

now replace on the first equation to solve r

`\begin{gathered} 2g+6.50r=3331.50 \\ 2(930-r)+6.50r=3331.50 \\ 1860-2r+6.50r=3331.50 \\ 6.50r-2r=3331.50-1860 \\ 4.50r=1471.50 \\ r=(1471.50)/(4.50) \\ \\ r=327 \end{gathered}`

the number of reserved tickets is 327

now replace r=327 on the second equation to find g

`\begin{gathered} g+r=930 \\ g+(327)=930 \\ g=930-327 \\ g=603 \end{gathered}`

the number of general tickets is 603