# Re: Systems of Linear Functions

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Posted by MathBard on October 04, 2002 at 20:22:32:

In Reply to: Systems of Linear Functions posted by bkone on October 04, 2002 at 19:03:17:

: I am having a real difficult time trying to understand these problems when they are in a story problem type scenerio. Here is my problem I am really needing help with:
: A sporting goods company can produce a football for \$12. The daily fixed costs are \$720, and the company plans to sell each football for \$20.
: The question is: What is the profit or loss if 200 balls are sold in a day? and What is the profit or loss for 300 footballs? How many balls must they sell to produce a daily profit of \$200?
: Could you also give me a quick summary on how you figured it out if you respond so I can try it on the others I have? Thanks

i like to make it into a verbal statement: simple first,then chunk-by-chunk then "translate" that into math.

VERBAL
Income - outgo = Profit/loss (i know? duh!)
Income = retail price * number sold
AND outgo = cost to make * number made PLUS fixed expenses. However subtract cost to make and subtract fixed expenses from outgo one at a time for ease.
all together that is ...
(retail price)*(footballs)-[(footballs)*(cost to make)] - (fixed expenses)= profit/loss

now fill in numbers that you know and define a variable for what varies. Hence the name!

p= profit/loss
n= number of footballs that day
20n-12n-720= P

sub 200 in for n. If p is positive, then that is your profit. A negative profit is a loss.
20(200)-12(200)-720= p
4000-2400-720=p
880=p woohoo a profit!
You can do the same for 300.

Now you can use your formula to work the OTHER way. For a \$200 daily profit sub in 200 for P and solve for N.

20N-12N-750=200
8n-750=200
8n=950
n=118.75 footballs
since you couldnt make or sell 3/4 of a football, 119 footballs would earn you a \$202 profit
118 footballs would earn you a \$194 profit

good luck
MathBard.

PS. i once had to write an 500-800 word essay narrating how to solve a stroy-problem about how much it would cost me to buy the right amount of paint that it would take to cover a certain barn of which i had to calculate its surface area.
AN essay plus a story problem how diabolical!

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