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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.)

Respuesta :

we can write a equation for each statement

The receipts were $3331.50

[tex]2g+6.50r=3331.50[/tex]

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

930 paid admissions

[tex]g+r=930[/tex]

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

[tex]g=930-r[/tex]

now replace on the first equation to solve r

[tex]\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=\frac{1471.50}{4.50} \\ \\ r=327 \end{gathered}[/tex]

the number of reserved tickets is 327

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

[tex]\begin{gathered} g+r=930 \\ g+(327)=930 \\ g=930-327 \\ g=603 \end{gathered}[/tex]

the number of general tickets is 603

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