Question 1

Question

A)
Use the table to answer the question.
Number of Cases Ordered Number of Rolls of Paper Towels
1
3
5
10
12
36
60
120
A restaurant is placing an order for paper towels. The data table shows the amount of paper
towel rolls compared to the number of cases. At which ratio in the data table does the constant
of proportionality appear? Write your answer as an ordered pair inside the parentheses
provided.
(1 point)

Answer 1

To determine the constant of proportionality from the data table you provided, we need values for the number of cases ordered and the number of rolls of paper towels.

If you assume that the number of rolls of paper towels is proportional to the number of cases ordered, we can find the ratio by dividing the number of rolls of paper towels by the number of cases ordered for each value.

Without the specific data from your table, I can guide you on how to calculate it. For each case in your data:

1. Divide the number of rolls of paper towels by the number of cases ordered.
2. Look for a consistent ratio across the different cases.

For example, if the ratio is consistently the same (let's say 12 rolls per case), then your ordered pair will reflect that ratio, which you can present as (cases, rolls), like (1, 12) if that’s your consistent ratio.

If you provide the specific numbers of cases ordered and rolls of paper towels, I can give you the exact ordered pair.

Answer 2

Question 2
A)
Use the table to answer the question.
Buses Number of People
0
1
2
3
4
0
35
70
105
140
A tour bus company is planning a trip through Utah’s national parks. The company plans to use
4 buses. Combined, the buses can fit up to 140 people. The table provided displays the
number of people-to-bus ratio. At which ratio in the data table does the constant of
proportionality appear? Write your answer as an ordered pair inside the parentheses provided.

Answer 3

To determine the constant of proportionality from the table you're referencing, we can analyze the provided data for the number of buses and the number of people.

From the information you've given:

• Buses: 0, 1, 2, 3, 4
• Number of People: 0, 35, 70, 105, 140

These values suggest that as the number of buses increases, the number of people accommodated increases proportionally.

To find the constant of proportionality:

1. For each entry, divide the number of people by the number of buses (where the number of buses is not zero).

   Here are the calculations based on your table:

   • For 1 bus: \( \frac{35 \text{ people}}{1 \text{ bus}} = 35 \)
   • For 2 buses: \( \frac{70 \text{ people}}{2 \text{ buses}} = 35 \)
   • For 3 buses: \( \frac{105 \text{ people}}{3 \text{ buses}} = 35 \)
   • For 4 buses: \( \frac{140 \text{ people}}{4 \text{ buses}} = 35 \)

The constant of proportionality is 35 people per bus.

The ordered pair that reflects the ratio of the number of buses to the number of people can be taken as any of the pairs where the ratio is established, such as (1, 35) or (4, 140).

Since the prompt asks specifically about the ratio in context, you can write:

(4, 140)

This indicates that with 4 buses, there are 140 people, and the constant of proportionality is reflected in this ordered pair.

Answer 4

Question 3
A)
Use the table to answer the question.
Cups of Flour Loaves of Bread
1
2
3
4
1
2
1
1
2
1
2
A bakery is making loaves of French bread. The recipe calls for 2 cups of flour per loaf of
bread. The data table shows how much flour the bakery needs depending on the number of
loaves it intends to make. At which ratio in the data table does the constant of proportionality
appear? Write your answer as an ordered pair inside the parentheses provided.
(1 point)

Answer 5

To determine the constant of proportionality from the information provided about the cups of flour and loaves of bread, we can analyze the data you provided:

• Cups of Flour: 1, 2, 3, 4
• Loaves of Bread: 1, 2, 1, 1, 2, 1, 2

The recipe states that 2 cups of flour are needed per loaf of bread. Here’s how we can find the constant of proportionality:

1. From the recipe, we know that:
   • 1 loaf of bread requires 2 cups of flour.
   • Therefore, the ratio of cups of flour to loaves of bread will remain consistent.

Thus, calculating the ratio from your data:

• For 2 cups of flour (from the data points), you can make 1 loaf.
• For 4 cups of flour, you should be able to make 2 loaves of bread as per the recipe.

Looking at the consistent ratio based on the recipe:

• For every 2 cups of flour, you get 1 loaf of bread.

Now, to find the constant of proportionality in terms of the ratios given:

By checking pairs:

• For 2 cups of flour, there is 1 loaf → (2, 1)
• For 4 cups of flour, there are 2 loaves → (4, 2)

Both pairs (2, 1) and (4, 2) indicate that the constant of proportionality (which reflects how many loaves of bread can be made per cups of flour) is established.

To provide the answer in the format asked, using the pair that correctly represents the coefficients, you can write either:

(2, 1)

Or if you prefer to illustrate a pair with more quantity, you might choose:

(4, 2)

Both pairs show the relationship, but (2, 1) directly reflects the 2 cups for every loaf of bread. You can select either based on the context of your question; both are acceptable.

Answer 6

Question 3
A)
Use the table to answer the question.
Cups of Flour Loaves of Brea 1 2 3 4 1/2 1 1 2/1 2
A bakery is making loaves of French bread. The recipe calls for 2 cups of flour per loaf of
bread. The data table shows how much flour the bakery needs depending on the number of
loaves it intends to make. At which ratio in the data table does the constant of proportionality
appear? Write your answer as an ordered pair inside the parentheses provided.
(1 point)

Answer 7

Given the updated table you provided:

• Cups of Flour: 1, 2, 3, 4
• Loaves of Bread: 1/2, 1, 1, 2

The recipe specifies that 2 cups of flour are needed for 1 loaf of bread. This means the constant of proportionality can be derived based on the ratios of cups of flour per loaf.

To determine the constant of proportionality, we can analyze the ratios:

1. For 1/2 loaf:

   • Cups of Flour: 1
   • Loaves of Bread: 1/2
   • Ratio: \( \frac{1 \text{ cup}}{1/2 \text{ loaf}} = 2 \)

2. For 1 loaf:

   • Cups of Flour: 2
   • Loaves of Bread: 1
   • Ratio: \( \frac{2 \text{ cups}}{1 \text{ loaf}} = 2 \)

3. For 1 loaf again:

   • Cups of Flour: 2
   • Loaves of Bread: 1
   • Ratio: \( \frac{2 \text{ cups}}{1 \text{ loaf}} = 2 \)

4. For 2 loaves:

   • Cups of Flour: 4
   • Loaves of Bread: 2
   • Ratio: \( \frac{4 \text{ cups}}{2 \text{ loaves}} = 2 \)

The constant of proportionality is consistently 2 cups of flour for every loaf of bread.

In terms of ordered pairs that represent the constant of proportionality, you can select:

(2, 1)

or

(4, 2)

Both pairs indicate the relationship defined by the recipe. The ordered pair (2, 1) explicitly shows that 2 cups of flour make 1 loaf of bread, which is a clear representation of the constant of proportionality in this context.