a store bought some calculators for $400 wholesale and sold all but 10 of them retail for $280 total. The store paid a whole number of dollars for each and received a whole number of dollars each week. If the store made a profit on the sale of each calculator how many calculators did the store originally have?

Question

a store bought some calculators for $400 wholesale and sold all but 10 of them retail for $280 total. The store paid a whole number of dollars for each and received a whole number of dollars each week. If the store made a profit on the sale of each calculator how many calculators did the store originally have?

Answer 1

Number of calulators: n

Price payed for each: p
Price received for each: r

Given:
p, r are integers. r > p
n p = 400
(n-10) r = 280
.:
(40/p -1)r = 28
.:
r = 28p/(40-p)

Find the positive integer solution when r>p.
Then use: n = 400/p

Answer 2

To find out how many calculators the store originally had, we need to analyze the given information.

Let's denote the number of calculators the store originally had as "x."

We know that the store bought the calculators for $400 wholesale. Since the store made a profit on the sale of each calculator, we can assume that the purchase price per calculator is less than the selling price.

Let's assume the store paid $y for each calculator. Now, we need to find the profit made on the sale of each calculator.

Profit per calculator = Selling price per calculator - Wholesale cost per calculator

Since the selling price for all but 10 calculators was $280 in total, the selling price per calculator can be found by dividing $280 by the total number of calculators sold.

Selling price per calculator = $280 / (x - 10)

Now, we can calculate the profit made on the sale of each calculator:

Profit per calculator = ($280 / (x - 10)) - y

Since the store made a profit on each calculator, we can assume that the profit is a positive integer. Therefore, y must be less than $280 / (x - 10).

But we also know that the store paid a whole number of dollars for each calculator. So, we need to find a value of y that is less than $280 / (x - 10) and is also a whole number.

We can start by assuming that y is 1, and calculate the resulting profit per calculator. If the profit is a positive integer, we have found our answer. If not, we can increment y by 1 and try again until we find a suitable value.

Using this approach, we can iterate through various values of y and calculate the corresponding profit per calculator until we find a value of y that results in a positive integer profit. By doing so, we can determine the number of calculators the store originally had.