Bunuel
At a sandwich shop, all sandwiches sell for the same price. If the shop were to decrease the price of each sandwich, it would sell 5 more sandwiches per day its daily revenue would remain constant at $150. How much does a sandwich currently cost?
A. $3
B. $4
C. $5
D. $6
E. $10
We know that the quantity sold is a whole number, and if we are also assuming that the price is a whole number (which is suggested by the answer choices), we can write 150 as the product of two positive integers as follows (where the first integer represents price and the second represents quantity):
150 = 1 x 150 = 2 x 75 = 3 x 50 = 5 x 30 = 6 x 25 = 10 x 15
We see that if the price is $6, then 25 sandwiches will be sold, and if we reduce the price by $1, then 30 sandwiches will be sold, which is exactly 5 more sandwiches than before. So, the current price must be $6.
Alternate Solution:
We will test each answer choice, except for choice B (since 150 is not divisible by 4).
If the original prices of the sandwiches are 3, 5, 6, or 10 dollars, then the shop originally sells 50, 30, 25, or 15 sandwiches, respectively.
We are given that the shop sells 5 more sandwiches by reducing the price, which means it will sell 55, 35, 30, or 20 sandwiches. Of these prices, 150 is divisible only by 30; therefore, 25 sandwiches must have been sold originally, which corresponds to a price of 6 dollars.
Answer: D