Question

A manufacturer makes and sells 2 products, P and Q. The revenue from the sale of each unit of P is 20.00 and the revenue from the sale of each unit of Q is 17.00. Last year the manufacturer sold twice as many units of Q as P. What was the manufacturer's average (arithmetic mean) revenue per unit sold of these 2 products last year? [Official GMAT-2018]

Hint:

To find the average revenue per unit, divide the total revenue by the total number of units sold. The revenue from each product depends on the units sold and the price per unit.

Answer 1

Step 1: Define the variables.
Let the number of units of P sold be \( x \). Since the manufacturer sold twice as many units of Q as P, the number of units of Q sold is \( 2x \). Step 2: Calculate the total revenue for each product.
The total revenue from the sale of P is: \[ \text{Total revenue from P} = 20x \] The total revenue from the sale of Q is: \[ \text{Total revenue from Q} = 17 \times 2x = 34x \] Step 3: Calculate the total revenue.
The total revenue from both products is: \[ \text{Total revenue} = 20x + 34x = 54x \] Step 4: Calculate the total number of units sold.
The total number of units sold is: \[ \text{Total units sold} = x + 2x = 3x \] Step 5: Calculate the average revenue per unit sold.
The average revenue per unit sold is: \[ \text{Average revenue per unit} = \frac{\text{Total revenue}}{\text{Total units sold}} = \frac{54x}{3x} = 18 \] Step 6: Conclusion.
The average revenue per unit sold is $18.00.