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Algebra 1

7.7.5 Practice

Algebra 17.7.5 Practice
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Complete the following questions to practice the skills you have learned in this lesson.

Use the following scenario to answer questions 1 – 5.

Based on past musical productions, a theater predicts selling 400 − 8 p tickets when each ticket is sold at p dollars.

  1. Answer questions a–g to complete the middle column in the table to find out how many tickets the theater expects to sell and what revenues it expects to receive at the given ticket prices.
Ticket price (dollars) Number of tickets sold Revenue (dollars)

5

360

1800

10

a. _____

  

15

b. _____

  

20

c. _____

  

30

d. _____

  

45

e. _____

  

50

f. _____

  

p

g. _____

  
    1. When the price is $ 10 per ticket, what is the number of tickets sold?
    1. When the price is $ 15 per ticket, what is the number of tickets sold?
    1. When the price is $ 20 per ticket, what is the number of tickets sold?
    1. When the price is $ 30 per ticket, what is the number of tickets sold?
    1. When the price is $ 45 per ticket, what is the number of tickets sold?
    1. When the price is $ 50 per ticket, what is the number of tickets sold?
    1. When the price is p per ticket, what is the number of tickets sold?
  1. p ( 8 p − 400 )
  2. p ( 400 − 8 p )
  3. 400 − 8 p
  4. 392 p
  1. Answer questions a-g to complete the right column in the table to find out what revenues the theater expects to receive at the given ticket prices.
Ticket price (dollars) Number of tickets sold Revenue (dollars)

5

360

1800

10

 

a. _____

15

 

b. _____

20

 

c. _____

30

 

d. _____

45

 

e. _____

50

 

f. _____

p

 

g. _____
    1. When the price is $ 10 per ticket, what is the revenue in dollars?
    1. When the price is $ 15 per ticket, what is the revenue in dollars?
    1. When the price is $ 20 per ticket, what is the revenue in dollars?
    1. When the price is $ 30 per ticket, what is the revenue in dollars?
    1. When the price is $ 45 per ticket, what is the revenue in dollars?
    1. When the price is $ 50 per ticket, what is the revenue in dollars?
    1. When the price is p per ticket, what is the revenue in dollars?
  1. 392 p
  2. p ( 400 − 8 p )
  3. 400 − 8 p
  4. p ( 8 p − 400 )
  1. For which ticket price, listed in the table, will the theater earn no revenue?
  1. Calculate the lowest price of a ticket that the theater should sell the tickets for if it must earn at least $ 3 , 200 in revenue to break even (to not lose money) on the musical production. (The calculated value may not be listed in the table.)
  1. Calculate the highest price of a ticket that the theater should sell the tickets for if it must earn at least $ 3 , 200 in revenue to break even (to not lose money) on the musical production. (The calculated value may not be listed in the table.)
  1. A company sells running shoes. If the price of a pair of shoes in dollars is p , the company estimates that it will sell 50 , 000 − 400 p pairs of shoes.

    Which expression represents the revenue in dollars from selling running shoes if a pair of shoes is priced at p dollars?
  1. ( 49 , 600 p ) ⋅ p
  2. ( 50 , 000 p − 400 p )
  3. ( 50 , 000 p − 400 ) ⋅ p
  4. ( 50 , 000 − 400 p ) ⋅ p

Use the following scenario to answer questions 7 – 10.

The function f represents the revenue in dollars the school can expect to receive if it sells 220 − 12 x coffee mugs for x dollars each.

Here is the graph of f .

Parabola on grid. Horizontal axis, price in dollars, from 0 to 20. Vertical axis, revenue in dollars, from 0 to 1000. Parabola opens down. Vertex near 9 comma 1000. \(\(x\)-intercepts near 0 and 18 point 2.

  1. Select three statements that describe this situation.
  1. At $2 per coffee mug, the revenue will be $196.
  2. The school expects to sell 160 mugs if the price is $5 each.
  3. The school will lose money if it sells the mugs for more than $10 each.
  4. The school will earn about $1,000 if it sells the mugs for $10 each.
  5. The revenue will be more than $700 if the price is between $5 and $14.
  6. The expected revenue will increase if the price per mug is greater than $10.
  1. To the nearest hundred dollars, what is the maximum revenue for the mugs?
  1. Which is the approximate domain?
  1. x ≥ 0
  2. 0 ≤ x ≤ 1000
  3. 0 ≤ x ≤ 18
  4. 0 ≤ x ≤ 9
  1. Which is the approximate range?
  1. − ∞ < y ≤ 1000
  2. y ≤ 1000
  3. 0 ≤ y ≤ 1000
  4. 0 ≤ y < ∞
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