Question

Amari can spend at most $40 at the fair. It costs her $12 to enter the fair and $3 per ticket, t, to ride the rides.

What is the most amount of rides she can ride with the money she has? Enter your answer as a whole number.

Answer 1

To determine how many rides Amari can take, we need to set up an equation based on her budget.

1. The total amount she can spend is $40.
2. She pays $12 to enter the fair.
3. Each ticket for the rides costs $3.

First, we subtract the entry fee from her total budget:

\[
\text{Remaining money} = 40 - 12 = 28
\]

Next, we denote the number of tickets (rides) she can buy as \( t \). The cost for the tickets will be \( 3t \).

Now we can set up the inequality based on the remaining money after paying for the entry fee:

\[
3t \leq 28
\]

To find the maximum number of tickets \( t \), we solve the inequality:

\[
t \leq \frac{28}{3}
\]

Calculating this gives:

\[
t \leq 9.33
\]

Since \( t \) must be a whole number, we take the largest whole number less than or equal to 9.33, which is 9.

Lastly, we should verify that this number works with her budget:

- If Amari buys 9 tickets, the cost for those tickets is:

\[
3 \times 9 = 27
\]

- Her total expenditure would then be the entry fee plus the tickets:

\[
12 + 27 = 39
\]

Since $39 is within her budget of $40, she can indeed ride the rides.

Thus, the most amount of rides Amari can ride is:

\[
\boxed{9}
\]