popcorn sales

Question

_____________________
| fantastic flicks popcorn |
| 2 bags for $21.00. |
|____________________|

_____________________
| Perfect Picture Popcorn |
| y=9.95x |
|____________________|
Movie Mania Popcorn
______________________________________
| # of bags of popcorn | amount paid (in dollars) |
|______________________________________|
| 8 | 81.20 |
| 6 | 60.90 |
| 4 | 40.60 |
| 2 | 20.30 |
| _____________________________________ |

. the big screen popcorn
. . . y.__________________________________
120 |______|______|______|_______|_______|
105 |______|______|______|_______|_______|
90. |______|______|______|_______|_______|
75. |______|______|______|_______|_______|
60. |______|______|______|_______|_______|
45. |______|______|______|_______|_______|
30. |______|______|______|_______|_______|
15. |______|______|______|_______|_______|x
. . .0. . . . . .3 . . . . . 6 . . . . . 9 . . . . . 12 . . . . . 15
y = amount paid (in dollars)
x = # of bags of popcorn
determine the constant of proportionality (unit price) for a bag of popcorn at each theater remember to include the hundredths place for each unit price.
big screen: $_ per bag of popcorn
fantastic flicks: $_ per bag of popcorn
movie mania: $_ per bag of popcorn
perfect picture : $_ per bag of popcorn
the theater with the best deal for popcorn is _______ and the
theater with the worse deal for popcorn is _______
if you bought 3 bags of popcorn from each company, how much would you save by purchasing from perfect picture than from fantastic flicks. remember to include the hundredths place in your response. $__

Answer 1

To determine the constant of proportionality (unit price per bag of popcorn) for each theater, we'll first calculate the price per bag for each one based on the information provided.

1. Fantastic Flicks Popcorn

• Price for 2 bags = $21.00
• Price per bag = $21.00 / 2 = $10.50

2. Perfect Picture Popcorn

• Given the equation \( y = 9.95x \), where \( y \) is the amount paid and \( x \) is the number of bags.
• Price per bag = $9.95 (This is the price for one bag of popcorn.)

3. Movie Mania Popcorn

• We can calculate the price per bag using the amounts given.
• From the table:
  • For 2 bags: $20.30 -> Price per bag = \( 20.30 / 2 = 10.15 \)
  • For 4 bags: $40.60 -> Price per bag = \( 40.60 / 4 = 10.15 \)
  • For 6 bags: $60.90 -> Price per bag = \( 60.90 / 6 = 10.15 \)
  • For 8 bags: $81.20 -> Price per bag = \( 81.20 / 8 = 10.15 \)
• Therefore, the unit price for Movie Mania is $10.15 per bag.

4. The Big Screen Popcorn

• Based on the graph, let's use the data points to calculate the unit price.
• From the graph:
  • For 3 bags: approximately $30 (assuming linear based on the axis)
  • For 6 bags: approximately $60
  • For 9 bags: approximately $90
  • For 12 bags: approximately $105
  • For 15 bags: approximately $120
• Price per bag for 3 bags: \( 30 / 3 = 10.00 \)
• Price per bag for 6 bags: \( 60 / 6 = 10.00 \)
• Price per bag for 9 bags: \( 90 / 9 = 10.00 \)

Therefore, the unit price for The Big Screen is $10.00 per bag.

Summary of Unit Prices:

• Big Screen: $10.00
• Fantastic Flicks: $10.50
• Movie Mania: $10.15
• Perfect Picture: $9.95

Best and Worst Deals:

• The theater with the best deal for popcorn is Perfect Picture ($9.95).
• The theater with the worst deal for popcorn is Fantastic Flicks ($10.50).

Savings Calculation:

To find out how much you would save by purchasing from Perfect Picture rather than Fantastic Flicks for 3 bags:

1. Cost from Perfect Picture for 3 bags:

   • \( 3 \times 9.95 = 29.85 \)

2. Cost from Fantastic Flicks for 3 bags:

   • \( 3 \times 10.50 = 31.50 \)

3. Savings:

   • \( 31.50 - 29.85 = 1.65 \)

Thus, the amount saved by purchasing from Perfect Picture rather than from Fantastic Flicks is $1.65.

Final Answers:

• Big Screen: $10.00 per bag of popcorn
• Fantastic Flicks: $10.50 per bag of popcorn
• Movie Mania: $10.15 per bag of popcorn
• Perfect Picture: $9.95 per bag of popcorn
• The theater with the best deal for popcorn is Perfect Picture.
• The theater with the worst deal for popcorn is Fantastic Flicks.
• Savings by purchasing from Perfect Picture than from Fantastic Flicks: $1.65.

Answer 2

. the big screen popcorn
. . . y.__________________________________
120 |______|______|______|_______|_______|
105 |______|______|______|_______|_______|
90. |______|______|______|_______|_______|
75. |______|______|______|_______|_______|
60. |______|______|______|_______|_______|
45. |______|______|______|_______|_______|
30. |______|______|______|_______|_______|
15. |______|______|______|_______|_______|x
. . .0. . . . . .3 . . . . . 6 . . . . . 9 . . . . . 12 . . . . . 15
y = amount paid (in dollars)
x = # of bags of popcorn
determine the meaning of the point (9,90)
1. 9 represents______________
2. 90 represents________________
1. a. the unit rate for the graph
b. the number of bags of popcorn purchased when $90.00 is paid
c. the amount of money paid when 9 bags fo popcorn are purchased
2. a. the unit rate for the graph
b. the number of bags of popcorn purchased when $90.00 is paid
c. the amount of money paid when 9 bags fo popcorn are purchased
d. the amount of money paid when 90 bags of popcorn are purchased

Answer 3

To interpret the point (9, 90) from the graph for The Big Screen Popcorn, we can break down the coordinates:

1. The first coordinate (9) represents the number of bags of popcorn purchased.
2. The second coordinate (90) represents the total amount of money paid in dollars.

Now, let's match these interpretations to the options provided:

1. 9 represents:

• b. the number of bags of popcorn purchased when $90.00 is paid (since 9 bags corresponds to this amount in the context of the graph)

2. 90 represents:

• c. the amount of money paid when 9 bags of popcorn are purchased (since this point directly describes the cost for purchasing 9 bags)

Summary:

• 1. 9 represents: b. the number of bags of popcorn purchased when $90.00 is paid
• 2. 90 represents: c. the amount of money paid when 9 bags of popcorn are purchased

Answer 4

determine the point for the constant of proportionality
(_,_)

Answer 5

To determine the point that represents the constant of proportionality (unit price) for the popcorn sales based on the information provided earlier, we need to calculate this value based on the unit prices derived from your previous question.

The constant of proportionality (unit rate) can be represented as \((x, y)\) where:

• \(x\) is the number of bags purchased,
• \(y\) is the total amount paid.

We previously established that different popcorn vendors have the following unit prices:

1. Perfect Picture Popcorn: $9.95 per bag
2. The Big Screen Popcorn: $10.00 per bag
3. Movie Mania Popcorn: $10.15 per bag
4. Fantastic Flicks: $10.50 per bag

This means that for proportionate relationships, a quantifiable point corresponding to a number of bags and the amount would be handy.

Example Points for Each Theater

Using the unit prices to create points for \(x = 1\) bag as a base:

1. Perfect Picture Popcorn:

   • \( (1, 9.95) \)

2. The Big Screen Popcorn:

   • \( (1, 10.00) \)

3. Movie Mania Popcorn:

   • \( (1, 10.15) \)

4. Fantastic Flicks:

   • \( (1, 10.50) \)

Summary Points

Therefore, the constant of proportionality for the Perfect Picture Popcorn, which has the best price, can be represented by:

• Point: \( (1, 9.95) \)

If you're looking specifically for a definition across all vendors based on a regular price graph, you'd consider them similarly with \(x\) being the number of bags, and \(y\) reflecting the total payment based on that constant.

If you have a specific vendor in mind for which you want to define a proportionality point, please let me know!

Answer 6

. the big screen popcorn
. . . y.__________________________________
120 |______|______|______|_______|_______|
105 |______|______|______|_______|_______|
90. |______|______|______|_______|_______|
75. |______|______|______|_______|_______|
60. |______|______|______|_______|_______|
45. |______|______|______|_______|_______|
30. |______|______|______|_______|_______|
15. |______|______|______|_______|_______|x
. . .0. . . . . .3 . . . . . 6 . . . . . 9 . . . . . 12 . . . . . 15
y = amount paid (in dollars)
x = # of bags of popcorn
part a. consider the points (3,30) and (12,120)
the rise from (3,30) to (12,120)=__ enter your answer as a whole number.
the run from (3,30) to (12,120) =__ enter your answer as a whole number.
the slope of the line from (3,30) to (12,120) = rise/run =__. remember to simplify the slope
part b. consider the points (0,0) and (6,60)
the rise from (0,0) to (6,60) =__ enter your answer as a whole number.
the run from ( 0,0) to (6,60) =__ enter your answer as a whole number.
the slope of the line from (0,0) to (6,60) = rise/run =__. remember to simplify the slope
part c. compare the slopes from part a. part b.
the slop from (0,0) to (6,60) is _________ to the slope from (3,30) to (12,120)

Answer 7

Let’s evaluate the points and calculate the rise, run, and slopes for both parts as described in your question.

Part A: Points (3, 30) and (12, 120)

1. Rise from (3, 30) to (12, 120): \[ \text{Rise} = y_2 - y_1 = 120 - 30 = 90 \]

2. Run from (3, 30) to (12, 120): \[ \text{Run} = x_2 - x_1 = 12 - 3 = 9 \]

3. Slope of the line: \[ \text{Slope} = \frac{\text{Rise}}{\text{Run}} = \frac{90}{9} = 10 \]

Part B: Points (0, 0) and (6, 60)

1. Rise from (0, 0) to (6, 60): \[ \text{Rise} = y_2 - y_1 = 60 - 0 = 60 \]

2. Run from (0, 0) to (6, 60): \[ \text{Run} = x_2 - x_1 = 6 - 0 = 6 \]

3. Slope of the line: \[ \text{Slope} = \frac{\text{Rise}}{\text{Run}} = \frac{60}{6} = 10 \]

Summary of Calculated Values

Part A:

• The rise from (3, 30) to (12, 120) = 90
• The run from (3, 30) to (12, 120) = 9
• The slope from (3, 30) to (12, 120) = 10

Part B:

• The rise from (0, 0) to (6, 60) = 60
• The run from (0, 0) to (6, 60) = 6
• The slope from (0, 0) to (6, 60) = 10

Part C: Compare the Slopes

• The slope from (0, 0) to (6, 60) is equal to the slope from (3, 30) to (12, 120) since both slopes are 10.

Thus, the complete statements for your question are:

• The rise from (3,30) to (12,120) = 90.
• The run from (3,30) to (12,120) = 9.
• The slope of the line from (3,30) to (12,120) = 10.
• The rise from (0,0) to (6,60) = 60.
• The run from (0,0) to (6,60) = 6.
• The slope of the line from (0,0) to (6,60) = 10.
• The slope from (0,0) to (6,60) is equal to the slope from (3,30) to (12,120).