Problem Solving

In a certain candy store in New York, each orange candy costs 30 cents and a strawberry candy costs 40 cents. The store gives an offer that if a customer buys three candies then the cheapest amongst them will not be charged for. What is the difference in the discount received by a customer who buys 2 strawberry candies and an orange candy, and a customer who buys 2 orange candies and a strawberry candy?

A. $0
B. $0.1
C. $0.2
D. $0.3
E. $0.5

OA is A
What could be the best possible approach tom solve this question? An Expert explanation will be appreciated. Thanks

Hello Roland.

Let's take a look at your question.

There is something that is not clear in the wording. Watching the answers, this PS should be solved like this:

In each case, the orange candy is the cheapest, therefore in both cases, the discount will be 30 cents. Hence, the difference is $0. The correct answer is A.

But, according to the wording, the way it should be solved is the following:

We have that:
- Each orange candy costs 30 cents.
- Each strawberry candy costs 40 cents.

If a customer buys:
- 2 strawberry candies and an orange candy, the total cost will be 110 cents.
- 2 orange candies and a strawberry candy, the total cost will be 100 cents.

Since we know that the store gives the following offer: if a customer buys three candies then the cheapest amongst them will not be charged for, hence the amount paid for each customer is:
- 2 strawberry candies and an orange candy, the new total cost is 80 cents.
- 2 orange candies and a strawberry candy, the new total cost is 70 cents.

This implies that the percentage paid for each customer is:
$$-\ P_1=\frac{80\cdot100}{110}\approx73\%\ \ \ \ \Leftrightarrow\ \ discount_1=27\%.$$
$$-\ P_2=\frac{70\cdot100}{100}\approx70\%\ \ \ \ \Leftrightarrow\ \ discount_2=30\%.$$

The difference in the discount is 3%.

I hope these explanations may help you.

I'm available if you'd like a follow-up.