Can someone help with this word problem? I have a hard time with them?

Question

Diego Motors is a small car dealership. On average, it sells a car for
$25,000, which it purchases from the manufacturer for $22,000. Each month, Diego Motors pays $50,000 in
rent and utilities and $60,000 for salespeople’s salaries. In addition to their salaries, salespeople are paid a
commission of $500 for each car they sell. Diego Motors also spends $10,000 each month for local advertisements.
Its tax rate is 40%.

1. How many cars must Diego Motors sell each month to break even?

2. Diego Motors has a target monthly net income of $54,000. What is its target monthly operating income?
How many cars must be sold each month to reach the target monthly net income of $54,000?

Answer 1

There's a lot of information here that you need to sort through and figure out if its an income or expense. Once you've got that, the rest is easy.

The first question asks about break even. You'll need to know how much you're spending, and then figure out how much you're making. Look at the spending first - you spend $22,000 per car, $60,000 on salary, $500 per car on commissions, $10,000 on ads, and 40% on taxes (I'm assuming that's on the profits only). So what you have is:

Expenses = 22000c + 60000 + 500c + 10000 + 3000*c*40%
= 22500c + 70000 + 1200c
=23700c + 70000

I used c to represent the number of cars that are sold per month. The 3000 in the last term came from the profit margin ($25000 per car that costs $22000 = $3000 in profits).

The income that the company makes is solely based on the number of cars sold:

Income = 25000c

Thus, to break eve, we set both of these equal and solve for c, which is the number of cars that we need:

23700c + 70000 = 25000c
1300c = 70000
c = 53.84 cars

So you need to sell 54 cars to break even (you can't sell a fraction of a car, so we round up to the next whole number).

For your second question, your net income is found by taking income minus expenses:

Net Income = 25000c - (23700c + 70000)
54000 = 25000c - 23700c - 70000
124000 = 1300c
c = 95.38

So you need 96 cars to make $54,000 monthly.