Compare Proportional Relationships Quick Check

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Question
Use the table and image to answer the question.

Cookie A – Cookies per Cup of Sugar
Cups Cookies
2 80
3 120
4 160
An illustration shows Quadrant 1 of a coordinate plane. The x-axis is labeled Cups and ranges from 0 to 6 in one unit increments. The y-axis is labeled Cookies and ranges from 0 to 192 in 12 unit increments. The graph is titled Cookies per Cup of Sugar. A line connects six points plotted on the graph. The coordinates of the plotted points are left parenthesis 0 comma 0 right parenthesis, left parenthesis 1 comma 36 right parenthesis, left parenthesis 2 comma 72 right parenthesis, left parenthesis 3 comma 108 right parenthesis, left parenthesis 4 comma 144 right parenthesis, and left parenthesis 5 comma 180 right parenthesis. An upward arrow points to 1 on the x-axis.

The yields of cookies per cup of sugar for Cookie A and Cookie B are displayed in the table and the graph. Find the cookie that yields the most cookies from one cup of sugar. How many cookies does Cookie A and Cookie B make from one cup of sugar?

(1 point)
Responses

Cookie B makes more cookies than Cookie A. Cookie B makes 72 cookies, and Cookie A makes 40 cookies.
Cookie B makes more cookies than Cookie A. Cookie B makes 72 cookies, and Cookie A makes 40 cookies.

Cookie A makes more cookies than Cookie B from one cup of sugar. Cookie A makes 40 cookies, and Cookie B makes 36 cookies from one cup of sugar.
Cookie A makes more cookies than Cookie B from one cup of sugar. Cookie A makes 40 cookies, and Cookie B makes 36 cookies from one cup of sugar.

Cookie A makes more cookies than Cookie B from one cup of sugar. Cookie A makes 80 cookies, and Cookie B makes 36 cookies from one cup of sugar.
Cookie A makes more cookies than Cookie B from one cup of sugar. Cookie A makes 80 cookies, and Cookie B makes 36 cookies from one cup of sugar.

Cookie B makes more cookies than Cookie A. Cookie B makes 40 cookies, and Cookie A makes 36 cookies from one cup of sugar.
Cookie B makes more cookies than Cookie A. Cookie B makes 40 cookies, and Cookie A makes 36 cookies from one cup of sugar.
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1 answer

To determine which cookie yields the most cookies from one cup of sugar, we need to analyze the data provided for both Cookie A and Cookie B.

From the table for Cookie A:

  • Cups: 2, Cookies: 80
  • Cups: 3, Cookies: 120
  • Cups: 4, Cookies: 160

To find out how many cookies Cookie A yields from one cup of sugar, we can calculate the rate:

  1. When there are 2 cups of sugar, there are 80 cookies, so: \[ \text{Cookies per cup} = \frac{80 \text{ cookies}}{2 \text{ cups}} = 40 \text{ cookies per cup} \]
  2. When there are 3 cups of sugar, there are 120 cookies, so: \[ \text{Cookies per cup} = \frac{120 \text{ cookies}}{3 \text{ cups}} = 40 \text{ cookies per cup} \]
  3. When there are 4 cups of sugar, there are 160 cookies, so: \[ \text{Cookies per cup} = \frac{160 \text{ cookies}}{4 \text{ cups}} = 40 \text{ cookies per cup} \]

From these calculations, we see that Cookie A makes 40 cookies per cup of sugar.

For Cookie B, we can read from the graph:

  • At 1 cup of sugar, the graph indicates that Cookie B makes 36 cookies.

Now, we compare the two results:

  • Cookie A: 40 cookies per cup of sugar
  • Cookie B: 36 cookies per cup of sugar

Based on this analysis:

  • Cookie A makes more cookies than Cookie B from one cup of sugar. Cookie A makes 40 cookies, and Cookie B makes 36 cookies from one cup of sugar.

Therefore, the correct response is: Cookie A makes more cookies than Cookie B from one cup of sugar. Cookie A makes 40 cookies, and Cookie B makes 36 cookies from one cup of sugar.