Question

a merchant paid $300 for a shipment of x identical calculators. the merchant used two of the calculators as demonstrators and sold each of the others for $5 more than the average (arithmetic mean) cost of the x calculators. if the total revenue from the sale of the calculators was $120 more than the cost of the shipment, how many calculators were in the shipment?

Answer 1

There were 24 calculators in the shipment.

Finding The Number Of Calculators In The Shipment.

The total cost of the shipment = $300.

Number of calculators in the shipment = (x).

Average cost per calculator is (300/x).

Selling price for each calculator is $5 more than the average cost.

Therefore, the selling price per calculator is (300/x) + 5.

The total revenue from selling the calculators is the selling price per calculator multiplied by the number of calculators.

Total Revenue = x * ((300/x) + 5)

The problem states that the total revenue was $120 more than the cost of the shipment:

Total Revenue = Total Cost + 120

Substitute the expressions for total revenue and total cost:

x * (300/x) + 5) = 300 + 120

Solve for (x):

300 + 5x = 420

Subtract 300 from both sides:

5x = 420 - 300

5x = 120

Divide both sides by 5:

(5x/5) = 120/5

x = 24

Therefore, there were 24 calculators in the shipment.