At a county fair, an adult ticket sold for $6.00, a senior citizen’s ticket for $4.50, and a child’s ticket for $2.00. On Friday, the number of adults and senior citizen’s tickets sold was 5 more than the number of children’s tickets sold. The number of adult tickets sold was 5 more than three times the number of senior citizen’s tickets sold. Total receipts from the ticket sales were $335.00. How many children’s tickets were sold?

Question

At a county fair, an adult ticket sold for $6.00, a senior citizen’s ticket for $4.50, and a child’s ticket for $2.00. On Friday, the number of adults and senior citizen’s tickets sold was 5 more than the number of children’s tickets sold. The number of adult tickets sold was 5 more than three times the number of senior citizen’s tickets sold. Total receipts from the ticket sales were $335.00. How many children’s tickets were sold?

:( I don't get how to solve this... I have this:

a+s=5+c

a=5+3(s)

a+s+c=335... but I don't get the numbers... can someone explain?

Answer 1

Not the number of tickets a+s+c = 335, but the value of the tickets.

6.00a + 4.50s + 2.00c = 335.00

Now you have three equations in 3 variables (after clearing fractions:

a - c + s = 5
a - 3s = 5
12a + 4c + 9s = 670

(a,c,s) = (35,40,10)

Answer 2

To solve this problem, we need to set up a system of equations based on the given information. Let's go step by step:

Step 1: Define your variables.
Let's use the following variables:
a = number of adult tickets sold
s = number of senior citizen's tickets sold
c = number of children's tickets sold

Step 2: Write equations based on the given information.
From the problem statement, we can gather the following information:
- The number of adult and senior citizen's tickets sold on Friday was 5 more than the number of children's tickets sold. This can be expressed as a + s = c + 5.

- The number of adult tickets sold was 5 more than three times the number of senior citizen's tickets sold. This can be expressed as a = 3s + 5.

- The total receipts from the ticket sales were $335. This can be expressed as 6a + 4.5s + 2c = 335 (since the ticket prices are given).

So now we have two equations:
a + s = c + 5 ... (Equation 1)
a = 3s + 5 ... (Equation 2)

Step 3: Solve the system of equations.
To solve the system, we can use substitution or elimination method. Let's use substitution here:

Substitute Equation 2 into Equation 1:
(3s + 5) + s = c + 5
4s + 5 = c + 5

Now, subtract 5 from both sides:
4s = c

Substitute this into Equation 3:
6a + 4.5s + 2c = 335
6a + 4.5s + 2(4s) = 335
6a + 4.5s + 8s = 335
6a + 12.5s = 335

Step 4: Simplify and solve for variables.
Now we have two equations with two variables:
4s = c ... (Equation 3)
6a + 12.5s = 335 ... (Equation 4)

Substitute 4s for c in Equation 4:
6a + 12.5s = 335
6a + 12.5(4s) = 335
6a + 50s = 335

Now, we have a system of linear equations:
4s = c ... (Equation 3)
6a + 50s = 335 ... (Equation 5)

To solve Equation 3 and Equation 5 simultaneously, we can use any method like substitution or elimination. Let's use substitution:

From Equation 3, we can rewrite it as:
c = 4s

Substitute this into Equation 5:
6a + 50s = 335
6a + 50s = 335

Now, solve for variables:
Using Equation 2 to solve for a:
a = 3s + 5

Substitute this into Equation 5:
6(3s + 5) + 50s = 335
18s + 30 + 50s = 335
68s + 30 = 335
68s = 305
s ≈ 4.49

Since s represents the number of senior citizen's tickets, it cannot be a decimal value. Therefore, we must have made a mistake in our calculations. I apologize for this error. Please let me recalculate for you.