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Answer :
Final answer:
To determine the number of children and adults who attended the Davis Middle School play, a system of equations is set up and solved using the elimination method. The solution is that 159 adults and 87 children attended the play.
Explanation:
The student is tasked with finding out how many children and adults attended a play at Davis Middle School, given that the total attendance was 246 and the total money made was $325.50, with ticket prices being $1.50 for adults and $1.00 for children.
Step-by-step Solution
Let the number of adult tickets be represented by a and the number of children tickets by c. We can set up a system of equations to represent the given information:
- a + c = 246 (Total number of tickets sold)
- 1.50a + 1.00c = 325.50 (Total amount of money made)
To solve the system, we can use the substitution or elimination method. Let's use the elimination method:
- Multiply the second equation by 2 to eliminate the decimals: 3a + 2c = 651
- Multiply the first equation by 2: 2a + 2c = 492
- Subtract the first modified equation from the second: (3a + 2c) - (2a + 2c) = 651 - 492, which simplifies to a = 159.
- Substitute a = 159 into the first equation: 159 + c = 246, which simplifies to c = 87.
Therefore, there were 159 adults and 87 children who attended the play.
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