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
24 tacos
24 tacos
25 tacos
25 tacos
26 tacos
Responses
27 tacos
27 tacos
24 tacos
24 tacos
25 tacos
25 tacos
26 tacos
Answers
GPT-4o mini
To determine how many tacos can be ordered for $100, we start with the price per taco. Based on the sequence given (3.75, 7.5, 11.25, ...), we can see that the total cost increases by $3.75 for each additional taco.
We can express the total cost \( C \) for \( n \) tacos as:
\[
C = 3.75n
\]
To find out how many tacos can be purchased with $100, we set up the inequality:
\[
3.75n \leq 100
\]
Now, we can solve for \( n \):
\[
n \leq \frac{100}{3.75}
\]
Calculating this gives:
\[
n \leq 26.6667
\]
Since \( n \) must be a whole number (you can't order a fraction of a taco), we take the maximum whole number less than or equal to 26.6667, which is 26.
Thus, the maximum number of tacos that can be ordered with $100 is **26 tacos**.
We can express the total cost \( C \) for \( n \) tacos as:
\[
C = 3.75n
\]
To find out how many tacos can be purchased with $100, we set up the inequality:
\[
3.75n \leq 100
\]
Now, we can solve for \( n \):
\[
n \leq \frac{100}{3.75}
\]
Calculating this gives:
\[
n \leq 26.6667
\]
Since \( n \) must be a whole number (you can't order a fraction of a taco), we take the maximum whole number less than or equal to 26.6667, which is 26.
Thus, the maximum number of tacos that can be ordered with $100 is **26 tacos**.