Question

1. you are selling tickets for a high school play. student tickets cost $4.00 and general admission tickets cost $6.00. you sell 525 tickets and collect $2,876.00. how many of each type of tickets did you sell?

137 student tickets and 388 adult tickets
137 adult tickets and 388 student tickets
212 student tickets and 313 adult tickets

Explanation:

Step1: Define variables

Let \( s \) be the number of student tickets and \( g \) be the number of general admission (adult) tickets. We know two equations:

1. \( s + g = 525 \) (total number of tickets)
2. \( 4s + 6g = 2876 \) (total money collected)

From the first equation, we can express \( s = 525 - g \).

Step2: Substitute into the second equation

Substitute \( s = 525 - g \) into \( 4s + 6g = 2876 \):
\( 4(525 - g) + 6g = 2876 \)
Expand: \( 2100 - 4g + 6g = 2876 \)
Simplify: \( 2100 + 2g = 2876 \)
Subtract 2100: \( 2g = 2876 - 2100 = 776 \)
Divide by 2: \( g = \frac{776}{2} = 388 \)

Step3: Find \( s \)

Using \( s = 525 - g \), substitute \( g = 388 \):
\( s = 525 - 388 = 137 \)

So, 137 student tickets and 388 adult tickets. We can also check by plugging into the options:

• For option 1: \( 137\times4 + 388\times6 = 548 + 2328 = 2876 \), which matches.
• For option 2: Swapped, so \( 137\times6 + 388\times4 = 822 + 1552 = 2374

eq 2876 \)

• For option 3: \( 212\times4 + 313\times6 = 848 + 1878 = 2726

eq 2876 \)

Answer:

137 student tickets and 388 adult tickets (the first option)