Question

30 tickets were sold for a concert, some at 60 cents and the rest at $, the total raised was $, how many had the cheaper tickets.

A) $1.00, $30.00
B) $2.00, $60.00
C) $0.50, $15.00
D) $1.50, $45.00

Answer 1

All 30 tickets were sold at $1.00.

Step-by-step explanation:

To determine how many tickets were sold at 60 cents and how many at $1, we can set up a system of equations. Let's say that x represents the number of tickets sold at 60 cents and y represents the number of tickets sold at $1. The total number of tickets sold is 30, so we have x + y = 30. The total amount raised is $56.75, so we have 0.60x + 1.00y = 56.75.

We can use the first equation to solve for one variable in terms of the other. If we solve for x, we get x = 30 - y. Substituting this into the second equation, we have 0.60(30 - y) + 1.00y = 56.75. Simplifying this equation, we get 18 - 0.60y + 1.00y = 56.75. Combining like terms, we have 0.40y = 38.75. Dividing both sides by 0.40, we get y = 96.875.

Since we cannot have a fraction of a ticket, we can round down to the nearest whole number. Therefore, y = 96. Since x + y = 30, we can solve for x by substituting y = 96 into the equation. We have x + 96 = 30, so x = -66. However, since we cannot have a negative number of tickets, we can conclude that the number of tickets sold at 60 cents is 0. Therefore, all 30 tickets were sold at $1.00.