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optional - ungraded ch 3 practice quiz
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question 5
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finding inputs and outputs in a story context
you purchase 110 bottles of water for 12 dollars and plan to sell them at the carnival for 98 cents each.
your profit can be determined by the function $p(x)=0.98x - 12$ where $p$ represents your profit and $x$ represents the number of bottles of water sold. round your answers to the nearest hundredth as needed.
calculate $p(56)$
complete the following sentence to explain the meaning of your answer.
the profit from selling $square$ bottles of water is $square$ dollars.
find $x$ when $p(x)=66.4$
complete the following sentence to explain the meaning of your answer.
the profit from selling $square$ bottles of water is $square$ dollars.

Explanation:

Step1: Substitute $x=56$ into $P(x)$

$P(56) = 0.98(56) - 12$

Step2: Calculate the product first

$0.98 \times 56 = 54.88$

Step3: Subtract the fixed cost

$P(56) = 54.88 - 12 = 42.88$

Step4: Set $P(x)=66.4$ and solve for $x$

$0.98x - 12 = 66.4$

Step5: Isolate the term with $x$

$0.98x = 66.4 + 12 = 78.4$

Step6: Solve for $x$

$x = \frac{78.4}{0.98} = 80$

Answer:

Calculate $P(56)$:
The profit from selling 56 bottles of water is 42.88 dollars.

Find $x$ when $P(x)=66.4$:
The profit from selling 80 bottles of water is 66.4 dollars.