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Alexeev081 [22]
3 years ago
12

Mia is going out to eat with some friends and has a total of $15 to spend. She got a water to drink and plans to leave a $3 tip.

The price of the entrees range from $5.98 to $24.99. She must also remember that there is a 7% sales tax applied to the cost of her meal. The total cost she pays for her meal, including the tip, can be modeled by the function f(c), where c represents the price of the entree she orders.
The domain of the function is__ ≤ c ≤ __.

Mia's friend Clara loans her $5 so that Mia has more entrees to choose from on the menu. With this additional $5, the domain of the function representing the price of an entree Mia can afford is now __≤ c ≤ __.
Mathematics
1 answer:
Olin [163]3 years ago
5 0
1.  First we are going to find the cost function.
We know for our problem that there is a 7% sales tax applied to the cost of her meal and she plans to leave 3$ as tip. Let c represent the cost of the meal:
f(c)=c+0.07c+3
f(c)=1.07c+3
where
c is the cost of the entree
f(c) is the total cost she will pay

We know that the minimum cost of an entree is $5.98, so the domain of our functions so far is: 5.98 \leq c \leq
Now, to find the upper limit of the domain, we are going to take advantage of the fact the she only has $15 to spend, so we can replace the total cost with 15 and solve for c:
f(c)=1.07c+3
15=1.07c+3
1.07c=12
c= \frac{12}{1.07}
c=11.21

We can conclude that the domain of the function is 5.98 \leq c \leq 11.21

2. We know that Mia's friend Clara loans her $5, so Mia's total money now is $15+$5=$20. Since the minimum cost for an entree remains the same ($5.98), the lower limit of our domain remains the same: 5.98 \leq c \leq
Now, to find the upper limit of our domain, we are going to replace the total cost with 20 an solve for c:
f(c)=1.07c+3
20=1.07c+3
1.07c=17
c= \frac{17}{1.07}
c=15.88

We can conclude that the domain of the function representing the price of an entree Mia can afford is now 5.98 \leq c \leq 15.88
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