Question

a survey asked 100 students what type of entertainment they wanted for their fall festival. partial results are shown in the table. complete the two - way table by determining the value of each letter.
frequency two - way table

	puppeteer	magician	total
boys	21	36	c
total	47	b	100

a =

b =

c =

26
41
53
57

Explanation:

Step1: Find \( a \)

For the "Girls" row, the total is the sum of "Puppeteer" and "Magician" counts. So \( a + 17 = 43 \). Solving for \( a \), we get \( a = 43 - 17 = 26 \).

Step2: Find \( b \)

For the "Magician" column, the total is the sum of "Girls" and "Boys" counts. So \( b = 17 + 36 = 53 \).

Step3: Find \( c \)

The total number of students is 100, and the total for girls is 43. So the total for boys \( c = 100 - 43 = 57 \). Also, we can check by adding "Puppeteer" and "Magician" counts for boys: \( 21 + 36 = 57 \), which matches.

Answer:

\( a = 26 \)
\( b = 53 \)
\( c = 57 \)