M7MBA wrote: ↑

Sat Sep 11, 2021 2:10 pm

A small business invests $9,900 in equipment to produce a product. Each unit of the product costs $0.65 to produce and is sold for $1.20. How many units of the product must be sold before the revenue received equals the total expense of production, including the initial investment in equipment?

A. 12,000
B. 14,500
C. 15,230
D. 18,000
E. 20,000

Answer: D

Source: Official Guide

Let x = the number of units produced AND sold

TOTAL COST
If each unit of the product costs $0.65 to produce, then it costs 0.65x dollars to produce x units
We must also add the $9,900 investment in equipment
So, TOTAL COST = 0.65x + 9900

TOTAL REVENUE
If each unit sells for $1.20 to produce, then selling x units results in TOTAL SALES of 1.2x dollars

We want: TOTAL REVENUE = TOTAL COST
In other words: 1.2x = 0.65x + 9900
Subtract 0.65x from both sides: 0.55x = 9900
Solve: x = 9900/0.55

PRO TIP: We know that 9900/0.5 = 19,800
Since 0.55 is a bit bigger than 0.5, we know that 9900/0.55 = a little bit LESS THAN 19,800

Answer: D

Cheers,
Brent