Receipts for a concert, attended by 450 people, were $2775. If reserved-seat tickets were $7 and general-admission tickets were $4, how many of each type of ticket were sold?

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- April 9th 2007, 11:06 AMPatiencesystem of equations word problem
Receipts for a concert, attended by 450 people, were $2775. If reserved-seat tickets were $7 and general-admission tickets were $4, how many of each type of ticket were sold?

- April 9th 2007, 11:15 AMJhevon
This is another application of simultaneous equations.

let the number of reserved tickets sold be r

let the number of general admission tickets sold be g

then the the money gained from selling reserved tickets is 7r and the money gained from selling general admission tickets is 4g. the total number of tickets sold is 450. so we have:

r + g = 450 ..................(1)

7r + 4g = 2775 .............(2)

4r + 4g = 1800 ..............(3) = (1)*4

7r + 4g = 2775 ..............(2)

3r = 975 .......................(4) = (2) - (3)

=> r = 975/3

=> r = 325

but r + g = 450

=> 325 + g = 450

=> g = 450 - 325

=> g = 125

so 325 reserved tickets were sold and 125 general admission tickets were sold