System of Linear Equations Word Problem - Concert Tickets

Question

The register confirmed that $3,751.50 was taken in after a concert. The manager counted 250 ticket receipts. The price of a student ticket was $12.50, and the price of an adult ticket was $17.00.

How many student tickets were sold?

How many adult tickets were sold?

Answer 1

change the price to $16 for Adults. Odds are the problem has a typo, a 7 where a 6 should be

S+A =250

12.5S + 16A = 3,751.5

multiply 1st equation by 12.5

12.5S + 12.5A = 12.5(250)= 3,125

subtract last from 2nd equation to get

16A-12.5A = 4.5A = 3751.5-3125 = 626.5

A = 626.5/3.5 = 179 Adult tickets

S= 250-179 = 71 Student tickets

12.5(71)+16(179)

=887.5 + 2864

= 3751.5

if you use $17 for Adult price, the ticket numbers for A and S aren't integers, but fractions

Answer 2

Hi Joshua!

You're going to have two equations here.

# of Student tix + # of Adult tix = total tix

S + A = 250

$$ student tix + $$ adult tix = $$ total

12.50S + 17A = 3751.50

Solve the first equation for S:

S + A = 250

-S -S

-----------------

A = 250 - S

Plug in for A in the second equation

12.50S+17(250-S)=3751.50

Solve this for S. When you get S, then

you can plug into A = 250-S to get the

number of adult tickets.