To determine the maximum number of tacos that can be ordered with $100, we need to first identify the cost per taco.
From the given sequence:
- For 1 taco, the cost is $3.75.
- For 2 tacos, the cost is $7.50.
- For 3 tacos, the cost is $11.25.
- For 4 tacos, the cost is $15.00.
- For 5 tacos, the cost is $18.75.
We can see that the costs increase by $3.75 for each additional taco.
This forms an arithmetic sequence where:
- The first term (cost for 1 taco) is \( a = 3.75 \)
- The common difference (cost increase for each additional taco) is \( d = 3.75 \)
The total cost \( C(n) \) for \( n \) tacos can be expressed as: \[ C(n) = a + (n-1)d \] Substituting \( a \) and \( d \): \[ C(n) = 3.75 + (n-1) \cdot 3.75 \] Factoring out \( 3.75 \): \[ C(n) = 3.75n \]
Now we need to find the maximum number \( n \) such that: \[ C(n) \leq 100 \] Substituting \( C(n) \): \[ 3.75n \leq 100 \]
Now we solve for \( n \): \[ n \leq \frac{100}{3.75} \] Calculating the division: \[ n \leq 26.6667 \]
Since \( n \) must be a whole number (as you cannot order a fraction of a taco), we round down to the nearest whole number: \[ n \leq 26 \]
Therefore, the maximum number of tacos that can be ordered with $100 is 26 tacos.
So the answer is: 26 tacos.