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2 years ago

A group of friends wants to go to the amusement park. They have no more than $165

Mathematics

1 answer:

Oksi-84 [34.3K]2 years ago

3 0

Answer:

17.75x + 5.25 $\leq$ 165

x $\leq$ 9

Step-by-step explanation:

The total cost can be represented by 17.75x + 5.25, where x is the number of people.

They can only spend a maximum of $165, so a less than or equal sign has to be used.

The inequality will be 17.75x + 5.25 $\leq$ 165

Now, solve for x:

17.75x + 5.25 $\leq$ 165

17.75x $\leq$ 159.75

x $\leq$ 9

So, x $\leq$ 9 is the answer, meaning 9 people or less can go to the amusement park.

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Step-by-step explanation:

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. Dinah bought 3 packages of ground beef. The packages weigh 3 3/4 pounds, 1 1/8 pounds, and 2 1/2 pounds. How many pounds of gr

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Answer:

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Convert the fractions so that the denominators match.

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2 years ago

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The larger box is 5x bigger than the smaller one.

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3 years ago

Solve for B in the picture below

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Answer:

b= -48

Step-by-step explanation:

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2 years ago

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A scuba diving company currently charges $100per dive. On average, there are 30 customers per day. The company performed a study

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A. Total Revenue (R) is equal to price per dive (P) multiplied by number of customers (C). We can write $R=PC$ .

Per price increase is $20. So four price increase is $ $20*4=$80$ . Hence, price per dive is 100+80=$180.

Also per price increase, 2 customers are reduced from 30. For 4 price increases, $4*2=8$ customers are reduced. Hence, total customers is $30-8=22$ .

So Total Revenue is:

$R=180*22=3960$

B. Each price increase is 20. So x price increase is 20x. Hence, new price per dive would be equal to the sum of 100 and 20x.

Also per price increase, customers decrease by 2. So per x price increases, the customer decrease is 2x. Hence, new number of customers is the difference of 30 and 2x.

Therefor we can write the quadratic equation for total revenue as the new price times the new number of customers.

$R=(100+2x)(30-2x)=-40x^{2}+400x+3000$

C. We are looking for the point (x) at which the equation modeled in part (B) gives a maximum value of revenue (y). That x value is given as $x=-\frac{b}{2a}$ , where a is the coefficient of $x^{2}$ and b is the coefficient of x. So we have,

$x=-\frac{b}{2a}=- \frac{400}{(2)(-40)}=5$

That means, the greatest revenue is achieved after 5 price increases. Each price increase was 20, so 5 price increase would be $5*20=100$ . So the price that gives the greatest revenue is $100+100=200$ .

ANSWERS:

A. $3960

B. $R=-40x^{2}+400x+3000$

C. $200

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3 years ago