Question

The sequence 3.75, 7.5, 11.25, 15, 18.75, . . . represents the total cost a customer pays at a taqueria based on the number of tacos ordered. This means that the total cost for 1 taco is $3.75, for 2 tacos is $7.50, for 3 tacos is $11.25, and so on. What is the maximum number of tacos that can be ordered if a customer has $100 to spend?(1 point)
Responses

27 tacos
27 tacos

26 tacos
26 tacos

25 tacos
25 tacos

24 tacos

Answer 1

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**.