SOLUTION: The profit on a watch is given by {{{P = x^2 – 13x – 80}}}, where {{{x}}} is the number of watches sold per day. How many watches were sold on a day when there was a $50 loss?
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Question 119643: The profit on a watch is given by , where is the number of watches sold per day. How many watches were sold on a day when there was a $50 loss? Found 3 solutions by benbjlin, josmiceli, tangitehewagen:Answer by benbjlin(6) (Show Source):
You can put this solution on YOUR website! You need to set up the equation.
Based on your problem P = profit and and since there was a $50 loss, P = -50.
Set up the equation:
-50 = x^2 - 13*x - 80
Simplify by adding both sides by 50.
0 = x^2 - 13*x - 30
You can put this solution on YOUR website!
There are 2 values of x that solve the equations and
Only makes sense, so,
15 watches are sold on a day when there is a
$50 loss
You can put this solution on YOUR website! A $ loss means that profit is negative so set and so .
We add to both sides of the equation to get
which simplifies to
.
Now lets see if we can factor the right hand side .
The coefficient of the term is so we ask ourselves what factors of have a sum of .
The integer factors of are and , and , and , and , and , and , and , and .
A quick inspection tells us the factors of and add up to .
So we can rewrite as .
This means that either or which tells us that
or .
But what does this mean, perhaps we had 2 more watches returned than what we sold or we sold a net of 15 watches. In either case, we have a $50 loss.
(
