Questions: Jayla likes cotton candy, each serving of which contains 220 calories. To burn off unwanted calories, Jayla participates in her favorite activities, shown in the table, in increments of 1 hour and never repeats a given activity on a given day. Complete parts (a) through (c). Activity Symbol Calories Burned Per Hour Volleyball v 160 Golf g 260 Canoeing c 320 Swimming s 410 Running r 680 (a) On Monday, Jayla has time for no more than two hours of activities. List all of the possible sets of activities that would burn off at least the number of calories obtained from three cotton candies. Choose the correct choice. A. c, s, v, r, c, r, s, r B. r, v, s, g, c, g, s, c, s C. c, s, v, r, g, r, c, r, s, r D. r, g, s, c, s, v, r, g, r, c, r, s, r

Jayla likes cotton candy, each serving of which contains 220 calories. To burn off unwanted calories, Jayla participates in her favorite activities, shown in the table, in increments of 1 hour and never repeats a given activity on a given day. Complete parts (a) through (c). Activity Symbol Calories Burned Per Hour Volleyball v 160 Golf g 260 Canoeing c 320 Swimming s 410 Running r 680 (a) On Monday, Jayla has time for no more than two hours of activities. List all of the possible sets of activities that would burn off at least the number of calories obtained from three cotton candies. Choose the correct choice. A. c, s, v, r, c, r, s, r B. r, v, s, g, c, g, s, c, s C. c, s, v, r, g, r, c, r, s, r D. r, g, s, c, s, v, r, g, r, c, r, s, r
Transcript text: Jayla likes cotton candy, each serving of which contains 220 calories. To burn off unwanted calories, Jayla participates in her favorite activities, shown in the table, in increments of 1 hour and never repeats a given activity on a given day. Complete parts (a) through (c). \begin{tabular}{c|c|c} Activity & Symbol & Calories Burned Per Hour \\ \hline Volleyball & v & 160 \\ Golf & g & 260 \\ Canoeing & c & 320 \\ Swimming & s & 410 \\ Running & r & 680 \\ \hline \end{tabular} (a) On Monday, Jayla has time for no more than two hours of activities. List all of the possible sets of activities that would burn off at least the number of calories obtained from three cotton candies. Choose the correct choice. A. $\{c, s\},\{v, r\},\{c, r\},\{s, r\}$ B. $\{r\},\{\mathrm{v}, \mathrm{s}\},\{\mathrm{g}, \mathrm{c}\},\{\mathrm{g}, \mathrm{s}\},\{\mathrm{c}, \mathrm{s}\}$ C. $\{c, s\},\{v, r\},\{g, r\},\{c, r\},\{s, r\}$ D. $\{r\},\{g, s\},\{c, s\},\{v, r\},\{g, r\},\{c, r\},\{s, r\}$
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Solution

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Solution Steps

To solve this problem, we need to determine which combinations of activities can burn at least the calories from three servings of cotton candy, which is \(3 \times 220 = 660\) calories, within a maximum of two hours. We will consider all possible combinations of activities that can be done in one or two hours and calculate the total calories burned for each combination. We will then select the combinations that meet or exceed the 660-calorie requirement.

Step 1: Determine Calories from Cotton Candy

Jayla consumes 3 servings of cotton candy, each containing 220 calories. Therefore, the total calories consumed are: \[ 3 \times 220 = 660 \text{ calories} \]

Step 2: List Activities and Calories Burned

The activities and their respective calories burned per hour are:

  • Volleyball (\(v\)): 160 calories
  • Golf (\(g\)): 260 calories
  • Canoeing (\(c\)): 320 calories
  • Swimming (\(s\)): 410 calories
  • Running (\(r\)): 680 calories
Step 3: Calculate Possible Combinations

Jayla can participate in activities for a maximum of 2 hours. We need to find combinations of activities that burn at least 660 calories. The possible combinations of activities are:

  • \(\{v\}\)
  • \(\{g\}\)
  • \(\{c\}\)
  • \(\{s\}\)
  • \(\{r\}\)
  • \(\{v, g\}\)
  • \(\{v, c\}\)
  • \(\{v, s\}\)
  • \(\{v, r\}\)
  • \(\{g, c\}\)
  • \(\{g, s\}\)
  • \(\{g, r\}\)
  • \(\{c, s\}\)
  • \(\{c, r\}\)
  • \(\{s, r\}\)
Step 4: Identify Valid Combinations

We calculate the total calories burned for each combination and select those that meet or exceed 660 calories:

  • \(\{r\}\): 680 calories
  • \(\{v, r\}\): 160 + 680 = 840 calories
  • \(\{g, s\}\): 260 + 410 = 670 calories
  • \(\{g, r\}\): 260 + 680 = 940 calories
  • \(\{c, s\}\): 320 + 410 = 730 calories
  • \(\{c, r\}\): 320 + 680 = 1000 calories
  • \(\{s, r\}\): 410 + 680 = 1090 calories

Final Answer

The valid combinations of activities that burn at least 660 calories are: \[ \boxed{\{\{r\}, \{v, r\}, \{g, s\}, \{g, r\}, \{c, s\}, \{c, r\}, \{s, r\}\}} \] The correct choice is D.

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