Question

A seventh grade class is having a raffle to raise money for a field trip. They have already raised $300, and will raise $6 for every ticket they sell. How many tickets do they need to sell to raise exactly $324?
Let t be the number of tickets the class sells. Write an expression that represents the total amount of money the class raises.

Answer 1

To find how many tickets the class needs to sell to raise exactly $324, we can first express the total amount of money raised as a function of the number of tickets sold.

Let \( t \) be the number of tickets sold. The class has already raised $300. Each ticket sold raises an additional $6. Therefore, the total amount of money raised, \( R(t) \), can be expressed as:

\[
R(t) = 300 + 6t
\]

We need to determine how many tickets need to be sold to raise exactly $324. To do this, we set the total amount equal to $324:

\[
300 + 6t = 324
\]

Now, we can solve for \( t \):

1. Subtract $300 from both sides:
\[
6t = 324 - 300
\]
\[
6t = 24
\]

2. Divide both sides by 6:
\[
t = \frac{24}{6}
\]
\[
t = 4
\]

Thus, the class needs to sell **4 tickets** to raise exactly $324.