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gulaghasi [49]
3 years ago
14

John owns a hot dog stand. He has found that his profit is represented by the equation p(x)=-x^2+62x+77, with p being profits an

d x the number of hot dogs sold. How many hot dogs must he sell to earn the most profit?
Mathematics
2 answers:
dedylja [7]3 years ago
4 0
Using a graphing calculator you can find that the maximum is 1038, so the profit starts to decline at the t value for <span>1038</span>, which is 31


hram777 [196]3 years ago
4 0
We want to maximize the profit, p(x) = -x^2 + 62x + 77.  
The graph of this function is a parabola that opens down.  The x-coordinate of the vertex is x = -b/(2a), which here is x = -62 / (2*-1), or 31.  So, we'll maximize John's profit if we advise him to sell 31 hot dogs.
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Please help I am so confused
Ede4ka [16]

The total cost when 881 minutes is used is $477.50.

<h3>What are the equation that model the question?</h3>

a + 480b = 277 equation 1

a + 990b = 532 equation 2

Where:

  • a = flat fee
  • b = variable fee

<h3>What is the flat fee and the variable fee?</h3>

Subtract equation 1 from equation 2

510b = 255

b = 255 / 510

b = $0.50

In order to determine the flat fee, substitute for b in equation 1

a + 480(0.5) = 277

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<h3>What is the total cost when 881 minutes is used?</h3>

Total cost = flat fee + (variable cost x number of minutes spoken)

$37 + (881 x 0.5) = $477.50

To learn more about simultaneous equations, please check: brainly.com/question/25875552

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7 0
1 year ago
Henry is making a corn grits recipe that calls for 1/4 cup of corn grits for every 1/2 cup of water. How much water will he need
Archy [21]

Method 1:

\begin{array}{ccc}\dfrac{1}{4}\ \text{cup of corn}&-&\dfrac{1}{2}\ \text{cup of water}\\\\1\dfrac{1}{2}=\dfrac{3}{2}\ \text{cup of corn}&-&x\ \text{cup of water}\end{array}\qquad\text{cross multiply}\\\\\\\dfrac{1}{4}\cdot x=\dfrac{3}{2}\cdot\dfrac{1}{2}\\\\\dfrac{1}{4}x=\dfrac{3}{4}\qquad\text{multiply both sides by 4}\\\\\boxed{x=3}

<h3>Answer: Henry will need 3 cups of water.</h3>

Method 2:

\begin{matrix}\dfrac{1}{4}\ \text{cup of corn}&-&\dfrac{1}{2}\ \text{cup of water}&|\text{multiply both sides by 2}\\\\\dfrac{1}{2}\ \text{cup of corn}&-&1\ \text{cup of water}&|\text{multiply both sides by 2}\\\\1\ \text{cup of corn}&-&2\ \text{cup of water}&|\end{matrix}

\begin{matrix}\left(\dfrac{1}{2}+1\right)\ \text{cups of corn}&-&(1+2)\ \text{cups of water}\\\\1\dfrac{1}{2}\ \text{cups of corn}&-&3\ \text{cups of water}\end{matrix}

<h3>Answer: Henry will need 3 cups of water.</h3>
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