Question

Two coffee shops have the same pricing strategy in attempt to promote conservation and eliminate water. They ask that customers buy a reusable mug on their first visit, then bring it in every time after for refills. Long’s Coffee Shop sells a refill mug for $7.50. Each refill costs $1.10. Sal’s Coffee Shop sells a refill mug for $2.25 and each refill costs $1.35. How many cups of coffee can you buy at each shop, so that you would be paying the same amount?

Answer 1

At Long's Coffee Shop, you can buy 5 cups of coffee for the cost to break even. At Sal's Coffee Shop, you can buy 8 cups of coffee for the cost to break even.

Step-by-step explanation:

For Long's Coffee Shop:

The initial cost for the refill mug is $7.50, and subsequent refills cost $1.10 each. To find the break-even point, divide the initial cost by the difference in refill costs: $7.50 / ($1.35 - $1.10) = $7.50 / $0.25 = 30 refills. Since each refill corresponds to one cup of coffee, adding the initial purchase, you can buy 30 + 1 = 31 cups. Dividing the initial cost by the refill cost difference gives the number of refills needed before the total spent matches the competitor's price for the same quantity of refills.

For Sal's Coffee Shop:

The initial cost for the refill mug is $2.25, and subsequent refills cost $1.35 each. Using the same method, $2.25 / ($1.35 - $1.10) = $2.25 / $0.25 = 9 refills. Adding the initial purchase, you can buy 9 + 1 = 10 cups for the cost to be equivalent to the competitor's price.

Comparing the two shops, at Long's Coffee Shop, you'd buy 31 cups for the same cost as buying 10 cups at Sal's Coffee Shop. This cost equivalence illustrates how the initial price of the refill mug and the subsequent refill costs determine the break-even point, influencing the number of cups purchased to reach the same overall expense.