Question

a survey was conducted asking different students (sorted by grade) when they would prefer to have assemblies. the results are displayed in the table to the right.
use the table to match the variable on the left to its value on the right.
not all values will match to a variable.
morning afternoon total
grade 6 15 8 23
grade 8 x y 39
grade 10 12 z 38
total 45 55 100

Explanation:

Step1: Solve for \( x \)

The total number of students who prefer morning assemblies is 45. We know the number of Grade 6 and Grade 10 students who prefer morning assemblies are 15 and 12 respectively. So, we can find \( x \) (Grade 8 morning) by subtracting the sum of Grade 6 and Grade 10 morning from the total morning.

$$ x = 45 - 15 - 12 = 18 $$

Step2: Solve for \( y \)

The total number of students who prefer afternoon assemblies is 55. We know the number of Grade 6 students who prefer afternoon assemblies is 8. The total number of Grade 8 students is 39, and we found \( x = 18 \), so the number of Grade 8 afternoon is \( 39 - 18 = 21 \)? Wait, no, better to use total afternoon. Wait, total afternoon is 55, Grade 6 afternoon is 8, Grade 10 afternoon is \( z \). Wait, first find \( z \). Wait, Grade 10 total is 38, morning is 12, so \( z = 38 - 12 = 26 \). Then total afternoon is 8 (Grade 6) + \( y \) (Grade 8) + \( z \) (Grade 10) = 55. So \( 8 + y + 26 = 55 \), so \( y = 55 - 8 - 26 = 21 \). Alternatively, using Grade 8 total: Grade 8 total is 39, so \( x + y = 39 \), we know \( x = 18 \), so \( y = 39 - 18 = 21 \).

Step3: Solve for \( z \)

Grade 10 total is 38, and the number of Grade 10 morning is 12, so \( z \) (Grade 10 afternoon) is \( 38 - 12 = 26 \).

Answer:

\( x = 18 \), \( y = 21 \), \( z = 26 \)