[MOVED] It costs a craftsman $5 to make one medal, sold for

[Andre]

Am I writing the equation correctly?

Word problem: It costs a craftsman $5 to make one medal, sold for $(50 - x), where x is the number of medals. His fixed cost is $350. To make a profit each week, what are the possible number of medals he should make?

my response:

(50 - x)x - 5x +350
-x(sqared) +50x - 5x +350 (how do you write squared in computer??)
-x(squared) + 45x + 350
(x + 10) (x + 35)

solution 10 < x < 35

 

[tkhunny]

Maybe, but only by luck.

Profit(x) = (50 - x)x - 5x + 350

That's no good. You have the wrong sign on "350". As you have it, there is a subsidy for producing.
Did you mean "- (5x + 350)"? That would have worked.

-x(squared) + 45x + 350
(x + 10) (x + 35)
solution 10 < x < 35

This is nearly magic.

1) (x + 10) (x + 35) = x^2 + 45x + 350. Where did the negative out front wander off?
2) (x + 10) (x + 35) = 0 leads to x = -10 and x = -35. How did you get positive values out of that?

In other words, this may be the only example of THREE errors that still managed to end up with ALMOST the right answer.

Your answer 10 < x < 35 is not quite satisfactory. Does 11.254 work? You need to restrict additionally to Whole Numbers.