Let's denote the number of adult admissions as 'a' and the number of youth admissions as 'y'.
According to the given information, the admission fee for an adult is $8.00 and the admission fee for a youth is $4.50. We know that the total number of admissions purchased was 209.
Therefore, we can write the following equation to represent the total number of admissions:
a + y = 209
Similarly, the total receipts from admission were $1304.50. We can represent this information with the following equation:
8a + 4.50y = 1304.50
Now, we have a system of linear equations:
Equation 1: a + y = 209
Equation 2: 8a + 4.50y = 1304.50
We can use substitution to solve this system.
From Equation 1, we can express y in terms of a:
y = 209 - a
Substituting this expression for y in Equation 2, we have:
8a + 4.50(209 - a) = 1304.50
Simplifying this equation, we get:
8a + 940.5 - 4.5a = 1304.50
3.5a + 940.5 = 1304.50
3.5a = 364
a = 104
Therefore, 104 adult admissions were purchased at the local fair.
Create a linear system to model this situation. Then use substitution to solve the linear system to solve the problem. At the local fair, the admission fee is $8.00 for an adult and $4.50 for a youth. One Saturday, 209 admissions were purchased, with total receipts of $1304.50. How many adult admissions were purchased
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