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
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.