word problems?

Question

to produce a game, it costs $0.95
the fixed costs is $6000
price per game is $1.69

(a) write total costs as a function of the # of games sold.

(b) write verage cost per unit c= c/x as a function of x.

THERE IS A LINE OVER THE FIRST C BEFORE THE EQUAL SIGN.

Please explain these. I also have no clue what the second question means.

Thank you so much!

Answer 1

Word problems-God's way of reminding us all that we're not as smart as we think we are!
For your first problem, the student is expected to know they Total Costs = Fixed Costs + Variable Costs. In other words, it costs $6000 just to start up, and then $0.69 for every game made.

Now at this point I must tell you that I don't like the way the problem is worded. "as a function of the # of games sold". Sold to whom? The stores? The wholesaler? The final customer?The information"price per game is $1.69" is of no use to us whatsoever, as the question of profit is never asked. Ah well, enough ranting.

Let C = total costs.
Let c = production cost per game
Therefore C = 6000 + 0.95c

For c=c/x, my take on the c bar is that it means "average cost". For clarity let me call it V
V=c/x . They want this equation re-arranged so that x is all by itself, with a +1 as its coefficient, and "on top", so to speak. As it stands now, it's "on the bottom.

V=c/x
Vx=c (mult. both sides by x)
x=c/ V (divide both sides by V)

That's it. I sincerely hope this helps. If they tell you you're wrong and the problem really meant something we missed, it's OK to smile sweetly but
consider murder.
Good luck!

Answer 2

(a) c = $6,000 + $1.69x
(b) let m = c-with-a-bar-over-it
m = c/x
m = ($6,000 + $1.69x)/x = $6,000/ x + $1.69