We are asked to determine which of the given market pricing guides is based on a constant . Let's check whether the relationship between the number of oranges and total cost is for each market, one by one.
Let's calculate the unit price of an orange by the total cost by the number of oranges.
Recall that two quantities are proportional if they have a constant or unit rate. For relationships in which this ratio is not constant, the two quantities are not proportional. Notice that the unit prices that we got are not the same, which means that the relationship between the number of oranges and total cost is not proportional.
Option B
Now let's take a look at the table from Option B.
| Number of Oranges
|
5
|
10
|
15
|
20
|
| Total Cost ($)
|
3.50
|
6.50
|
9.50
|
12.50
|
Similar to before, we will calculate the unit price by dividing the total cost by the number of oranges.
| Number of Oranges
|
5
|
10
|
15
|
20
|
| Total Cost ($)
|
3.50
|
6.50
|
9.50
|
12.50
|
| Unit Price ($ per orange)
|
3.50/5=0.70
|
6.50/10=0.65
|
9.50/15≈ 0.63
|
12.50/20=≈ 0.63
|
In this case, the unit prices are not the same, so the relationship between the number of oranges and total cost is not proportional.
Option C
Consider the pricing guide from Option C.
| Number of Oranges
|
5
|
10
|
15
|
20
|
| Total Cost ($)
|
3.00
|
5.00
|
7.00
|
9.00
|
Let's find the unit prices!
| Number of Oranges
|
5
|
10
|
15
|
20
|
| Total Cost ($)
|
3.00
|
5.00
|
7.00
|
9.00
|
| Unit Price ($ per orange)
|
3.00/5=0.60
|
5.00/10=0.50
|
7.00/15≈ 0.47
|
9.00/20=0.45
|
Since the unit prices are not the same, the relationship between the number of oranges and total cost is not proportional.
Option D
Finally, we will consider the table from option D.
| Number of Oranges
|
5
|
10
|
15
|
20
|
| Total Cost ($)
|
3.00
|
6.00
|
9.00
|
12.00
|
Let's calculate the unit price for each number of oranges.
| Number of Oranges
|
5
|
10
|
15
|
20
|
| Total Cost ($)
|
3.00
|
6.00
|
9.00
|
12.00
|
| Unit Price ($ per orange)
|
3.00/5=0.60
|
6.00/10=0.60
|
9.00/15=0.60
|
12.00/20=0.60
|
As we can see, all of the unit prices are equal to $0.60 per orange, which means that the relationship between the number of oranges and total cost is proportional.
Summary
We got that only the guide from Option D is based on a constant unit price. This means that the correct option is D.
