Question

Yami is a business representative of a beauty soap. The company gives her a weekly allowance of \[\$ 300\] to spend on lunches with owners of salons and their staff. Yami is a regular visitor to the restaurant AROMAS. The restaurant charges 7 for cold dish 11 for a hot dish including drinks. If each meal costs 5.75% sales tax, which of the following inequalities represents the number of cold dishes (c) and hot dishes (h) that Yami can purchase from AROMAS in one week?
A. $7c + 11h \leqslant 1.0575(300)$
B. $7c + 11h \geqslant 1.0575(300)$
C. \[1.0575(7c + 11h) \leqslant 300\]
D. \[1.0575(7c + 11h) \geqslant 300\]

Answer 1

Hint: We will first find the normal costs using the cost given which is charged by the restaurant AROMAS. After this, we now need to add the tax cost of all the meals in the original cost and thus, we have the required answer.

Complete step-by-step answer:
We see that the starting information in the question tells us that Yami is given an allowance of \[\$ 300\] to spend. So, whatever be the outcome money spent, it must be definitely less than or equal to 300.
Now, looking at the options we can clearly see that, we only have two options which are satisfying this condition which are (A) and (C). Therefore, (B) and (D) are discarded.
Now, since we are provided with the information that the restaurant charges 7 for cold dish and 11 for hot dish (including drinks) and c represents the number of cold dish and h represents the number of hot dishes.
Since 1 hot dish costs 7.
$\therefore $ h hot dishes cost 7h.
Similarly, 1 cold dish costs 11.
$\therefore $ c cold dishes cost 11c.
$\therefore $ the total cost for hot and cold dishes together will be 7h + 11c.
Now, we just need to find the tax value she has to pay for all the meals.
Since the tax value is 5.75%.
$\therefore $ the tax amount is \[\dfrac{{5.75}}{{100}}(7h + 11c)\].
Adding both of the amounts that is the original cost and tax cost, we will get:-
$\therefore Amount = 7h + 11c + \dfrac{{5.75}}{{100}}(7h + 11c)$
Simplifying the RHS, we will get:-
$ \Rightarrow Amount = 7h + 11c\left( {1 + \dfrac{{5.75}}{{100}}} \right)$
Simplifying the RHS further, we will get:-
$ \Rightarrow Amount = 7h + 11c\left( {\dfrac{{105.75}}{{100}}} \right)$
Simplifying the RHS again, we will get:-
$ \Rightarrow Amount = 7h + 11c\left( {1.0575} \right)$
Now, we already discussed that this needs to be less than or equal to 300.
$\therefore \left( {7h + 11c} \right)1.0575 \leqslant 300$

Hence, the correct option is (C).

Note: The students might make the mistake of finding the value of tax but forget to add the original cost excluding tax to it, which will bring a differing answer.
The students must keep in mind to check whether we are given a weekly or month allowance in the question so as to make no mistake, if she is given a month allowance, then we will require to find weekly using it by dividing it by 4 and thus using the resulting amount in the final solution.