SOLUTION: Please help me solve this word problem. Write a system of the questions and then solve using the method of your choice the reserve seat tickets for the football game cost fou

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Question 1104845: Please help me solve this word problem.
Write a system of the questions and then solve using the method of your choice
the reserve seat tickets for the football game cost four dollars each and the general mission tickets three dollars each after the game is over there and end count shows 1787 people attended the game the total receipts were $5792. find the number of each kind of tickets sold.
Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
x = number of reserve tickets that cost 4 dollars each.
y = number of general admission tickets that cost 3 dollars each.

1787 tickets were sold.
total receipts were 5792.

your equations are:

x + y = 1787
4x + 3y = 5792.

first equation models total number of tickets sold.
second equation models total amount of money received.

multiply the first equation by 4 and leave the second equation as is to get:

4x+ 4y = 7148
4x + 3y = 5792

subtract the second equation from the first to get:

y = 1356.

go back to the first original equation and solve for x to get x = 431.

go back to the second original equation and replace x with 431 and y with 1356 to get:

4*431 + 3*1356 = 5792

this confirms the solution is good.

431 + 1356 = 1787 which is what it's supposed to be.
4*431 +3*1356 = 5792 which is what it's supposed to be.