Question

The Northwest High School senior class decided to host a raffle to raise money for their senior trip. They charged $2 for each student raffle ticket and $5 for each adult raffle ticket and they raised $2,686 from ticket sales. If adults bought 3 times as many tickets as students, how many tickets did the senior class sell?

2x + 5y = 2,686

y = 3x

Northwest High School’s senior class sold
raffle tickets.

Answer 1

Let's denote:
- \( x \) as the number of student tickets sold,
- \( y \) as the number of adult tickets sold.

From the problem, we have the following two equations:
1. The total money raised from ticket sales:
\[
2x + 5y = 2686
\]
2. The relationship between adult and student tickets:
\[
y = 3x
\]

Now, we can substitute the second equation into the first equation to solve for \( x \).

Substituting \( y = 3x \) into the first equation gives:
\[
2x + 5(3x) = 2686
\]

This simplifies to:
\[
2x + 15x = 2686
\]
\[
17x = 2686
\]

Now, solve for \( x \):
\[
x = \frac{2686}{17}
\]
\[
x = 158
\]

Now, we can find \( y \) by substituting \( x \) back into the equation \( y = 3x \):
\[
y = 3(158) = 474
\]

Now, we have:
- \( x = 158 \) (student tickets),
- \( y = 474 \) (adult tickets).

To find the total number of tickets sold, we add the number of student tickets and adult tickets together:
\[
x + y = 158 + 474 = 632
\]

Thus, the Northwest High School senior class sold a total of **632** raffle tickets.