General tickets for a soccer game is 3.50 and reserved tickets are 5.00. 110 general tickets were sold than reserved ones and the total of tickets is 980-How many general tickets were sold?

Answer 1

This problem can be answered with a system of equations. Assign two variables for the unknowns, which are the number of general tickets sold, call that x, and the number of reserved tickets sold, call that y. The price of a general ticket is 3.5 and the price for a reserved ticket is 5. So 3.5x represents the total amount of money earned on the sale of general tickets. Similarly, 5y represents the total amount of money earned on the sale of reserved tickets. The total amount of money made at the game is 980. So you add together the money from general tickets, 3.5x, and the money from reserved tickets, 5y, and let that sum equal 980. Now you have your first equation: 3.5x + 5y = 980. The problem also states that 110 more general tickets were sold than reserved ones. We must express this statement in terms of x and y. The number of general tickets is 110 more than the number of reserved ones, so x = y +110. Now we have our second equation. We can solve the system of two equations with simple substitution. Substitute the expression y + 110 for x in the first equation. That gives: 3.5(y + 110) + 5y = 980. Now solve that equation for y. 3.5y + 385 + 5y = 980, therefore 8.5y = 595, and y = 70. But we're not done yet. y represents the number of reserved tickets sold. We are asked to find the number of general tickets sold. That's x. If x = y + 110, then x = 70 + 110; x = 180. There were 180 general tickets sold. Check: does 3.5(180) + 5(70) = 980? It does.