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

1 answer

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.