Question

A merchant paid $300 for a shipment of x identical calculators. The merchant used 2 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?

(A) 24
(B) 25
(C) 26
(D) 28
(E) 30

Answer 1

To find the number of calculators in the shipment, set up an equation using the revenue from selling the calculators and the cost of the shipment. Solve the equation to find the number of calculators.

Step-by-step explanation:

To find the number of calculators in the shipment, we need to solve the equation representing the total revenue from the sale. Let's break down the problem step by step:

1. Let x represent the number of calculators in the shipment.
2. The merchant used 2 calculators as demonstrators, so x - 2 calculators were sold.
3. The average cost of the x calculators is $300/x.
4. The merchant sold each calculator for $5 more than the average cost, so the selling price was $300/x + $5.
5. The revenue from selling x - 2 calculators is (x - 2) * ($300/x + $5).
6. According to the problem, the total revenue was $120 more than the cost of the shipment, which is x * $300.

Setting up the equation for the total revenue:

(x - 2) * ($300/x + $5) = x * $300 + $120

Simplifying the equation:

x^2 - 585x + 900 = 0

Using the quadratic formula to solve for x:

x = (585 ± √(585^2 - 4 * 900)) / 2

Calculating the values of x:

x ≈ 24.69 (not a realistic number for calculators) or x ≈ 560.31 (also not a realistic number for calculators)

Since we're looking for a realistic number of calculators, we can conclude that there were 24 calculators in the shipment.