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2 years ago

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Mrs. Huck is selling her own brand of roasted peanuts at a local amusement park where the profit P depends on the number of pean

ut bags sold B, and number of bags sold B depends on the number of visitors V to the amusement park. The following equations represent her scenario:
P = 10B - 150

B = 8(V - 5)

Write an equation for profit based on visitors.
P = ________

Write an equation for Profit using your answer from part (a).

Simplified Expression:
P= _________

Using your equations, find the profit if the number of visitors are 50 in a given day.

1 answer:

leva [86]2 years ago

4 0

Answer:

a) P = 10(8(V -5)) -150

b) P = 80V -550

c) P = 3450

Step-by-step explanation:

a) Use the expression for B to substitute into the equation for P:

P = 10(8(V -5)) -150

__

b) Eliminate parentheses and collect terms.

P = 10(8V -40) -150

P = 80V -400 -150

P = 80V -550

__

c) Substitute 50 for V and do the arithmetic.

P = 80·50 -550

P = 3450

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Step-by-step explanation:

We use a Venn Diagram to solve this question.

I am going to say that:

A are the students who like Mozart.

B are the students who like Beethoven

C are the students who like Haydn.

We have that:

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In which a are those who only like Mozart, $(A \cap B)$ are those who like Mozart and Beethoven, $(A \cap C)$ are those who like Mozart and Haydn and $(A \cap B \cap C)$ are those who like all three of them.

By the same logic, we have that:

$B = b + (A \cap B) + (B \cap C) + (A \cap B \cap C)$

$C = c + (B \cap C) + (A \cap C) + (A \cap B \cap C)$

We start finding these values from the intersection:

8 like all three composers

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This means that:

$(B \cap C) + (A \cap B \cap C) = 14$

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This means that:

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$(A \cap B) + (A \cap B \cap C) = 14$

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This means that C = 31. So

$C = c + (B \cap C) + (A \cap C) + (A \cap B \cap C)$

$31 = c + 6 + 13 + 8$

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This means that $B = 36$

So

$B = b + (A \cap B) + (B \cap C) + (A \cap B \cap C)$

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This means that A = 37. Then

$A = a + (A \cap B) + (A \cap C) + (A \cap B \cap C)$

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$(A \cap B) + (A \cap C) + (B \cap C) = 6 + 13 + 6 = 25$

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d. like Beethoven and Haydn, but not Beethoven?

I will use not Mozart.

So $B \cap C = 6$

Not Mozart, 6.

e. like none of these composers?

At least 1:

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The total is 65

So 65 - 63 = 2 like none of these composers

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