Math Problem on Linear Systems..?

Question

You are starting a business selling boxres of hand-painted greeting cards. To get started, you spend $36 on paint and paintbrushes that you need. You buy boxes of plain cards for $3.50 per box and then sell them for $5 per box. How many boxes must you sell for your earnings to equal expenses? What will your earnings equal when you break even. PLEASE SHOW YOUR WORK!

Answer 1

This is pretty straightforward. You should learn the method so you can do it yourself.

Let B be the number of boxes you sell.

First figure expenses (items bought):
$36.00 = paint and brushes bought
$3.50 x B = unfinished boxes bought

Next figure earnings (items sold):
$5.00 x B = painted boxes sold

Now equate them:
36.00 + 3.50B = 5.00B

Subtract 3.50B from both sides:
36 = 5B - 3.5B

Distribute B:
36 = (5 - 3.5)B
36 = 1.5B

Divide both sides by 1.5:
B = 36 / 1.5
B = 24

So you must sell 24 boxes to break even.

Earnings would just be 5.00B = 5 x 24 = $120.

Answer 2

Let the number of boxes be n.

$36 + $3.50 x n = $5 x n
36 = 1.5 x n
n = 24

earnings = 24 x $5 = $120