your class sells 64 tickets to a play.
A student ticket cost $1.
An adult ticket $2.50
If you collect $109 in total ticket sales, how many adult tickets do you sell? please show how to solve
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as with all word problems, translate the words to symbols. Then you have equations which can be solved.
If there are a adult and c child tickets, you have two sets of facts: the number of tickets and their cost.
c + a = 64
1.00c + 2.50a = 109.00
Now you can use your math skills to solve those equations.
number of adult tickets --- x
number of student tickets -- y
x + y = 64
2.5x + y = 109
subtract the two equations to get x = ...
then sub back into the first equation to get y
To solve this problem, we need to set up equations based on the given information.
Let's assume the number of adult tickets sold is "x" and the number of student tickets sold is "y."
From the problem statement, we know that a student ticket costs $1. So, the cost of all the student tickets can be calculated as 1 * y.
Similarly, an adult ticket costs $2.50, so the cost of all the adult tickets can be calculated as 2.5 * x.
Now, we know that the total ticket sales amount to $109. Therefore, we can set up the following equation:
1 * y + 2.5 * x = 109
Since you want to find the number of adult tickets sold, we need to find the value of "x" that satisfies the equation.
One way to proceed is to use trial and error. Since we have a limited number of tickets (64 in total), we can start trying different values of "x" (the number of adult tickets sold) and see if the equation holds true.
To simplify the calculations, let's substitute the equation as follows:
y + 2.5x = 109
Now, let's try a few values of "x" and calculate the corresponding value of "y":
For x = 0:
0 + 2.5 * 0 = 0
The ticket sales amount is 0, which is lower than the required $109. So, this is not the correct value for "x."
For x = 1:
y + 2.5 * 1 = 109
y + 2.5 = 109
y = 109 - 2.5
y = 106.5
However, the number of tickets (y) cannot be a decimal value as it represents the number of students. Therefore, this is also not the correct value for "x."
For x = 2:
y + 2.5 * 2 = 109
y + 5 = 109
y = 109 - 5
y = 104
Here, we have an integer value for "y" (the number of student tickets), so this is a potential solution. However, we need to verify that the total number of tickets sold is equal to 64:
x + y = 2 + 104 = 106
But the given total number of tickets is 64, which is not equal to 106.
As we can see, none of the values we have tried so far satisfies the given conditions.
Therefore, we need to try different values of "x" until we find the correct one that satisfies both equations.