To determine how many rides Amari can take, we need to set up an equation based on her budget.
- The total amount she can spend is $40.
- She pays $12 to enter the fair.
- 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:
\[ \boxed{9} \]
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