Question

members of a sports club are junior, adult or senior.
80 members were asked whether they prefer tea, coffee or hot chocolate.

25 members are senior, of which 13 prefer coffee.
10 juniors prefer tea.
there are no adult members who prefer hot chocolate.
2 of the 18 juniors prefer coffee.
4 of the 28 members who prefer tea are seniors.

what fraction of members in the club prefer hot chocolate?
give your answer as a fraction in its simplest form.

Explanation:

⚡ Using what you learned: Organizing Data in Tables

Step 1: Set up a two-way table

We can organize the information using a two-way table with categories for age group (Junior, Adult, Senior) and drink preference (Tea, Coffee, Hot Chocolate).

	Tea	Coffee	Hot Chocolate	Total
Adult
Senior
Total				80

Step 2: Fill in the given values

We fill in the table using the clues provided in the problem:

• Total members = \(80\)
• \(25\) members are senior: Senior Total = \(25\)
• Of those seniors, \(13\) prefer coffee: Senior & Coffee = \(13\)
• \(10\) juniors prefer tea: Junior & Tea = \(10\)
• No adult members prefer hot chocolate: Adult & Hot Chocolate = \(0\)
• There are \(18\) juniors in total: Junior Total = \(18\)
• \(2\) of those juniors prefer coffee: Junior & Coffee = \(2\)
• \(28\) members prefer tea in total: Tea Total = \(28\)
• Of those who prefer tea, \(4\) are seniors: Senior & Tea = \(4\)

	Tea	Coffee	Hot Chocolate	Total
Adult			\(0\)
Senior	\(4\)	\(13\)		25
Total	28			80

Step 3: Calculate the missing values

• Junior & Hot Chocolate:

$$ 18 - 10 - 2 = 6 $$

• Senior & Hot Chocolate:

$$ 25 - 4 - 13 = 8 $$

• Total Hot Chocolate:

Since there are \(6\) juniors, \(0\) adults, and \(8\) seniors who prefer hot chocolate:

$$ 6 + 0 + 8 = 14 $$

Step 4: Write the fraction in its simplest form

The fraction of members who prefer hot chocolate is:

$$ \frac{14}{80} = \frac{7}{40} $$

Answer:

\(\frac{7}{40}\)