Question

A student cafeteria has 24 tables, tables X has 4 seats each, tables Y has 6 seats each, and tables Z has 10 seats each. The total seating capacity of the cafeteria is 148. For a student meeting, half of tables X, 1/4 of tables Y, and 1/3 of tables Z will be used, for a total of 9 tables. Determine X, Y, and Z. ( Answer the final answer in a full sentence. )

Answer 1

Answer: For a meeting, half of x, 1/4 of y, and 1/3 of z will be used for a total of 9 tables:

`\begin{gathered} x+y+z=9 \\ \\ \\ \\ (1)/(2)x=(4)/(2)=2 \\ \\ (1)/(4)y=(6)/(4)=(3)/(2) \\ \\ (1)/(3)z=(10)/(3) \\ \\ \text{ Since we have a total of 9 tables therefore we have:} \\ \\ 3x+3y+3z\Rightarrow\text{ Total number of chairs.} \\ \\ 3(2)+3((3)/(2))+3((10)/(3))=6+(9)/(2)+10 \\ \\ \\ \text{Therefore:} \\ \\ ------------------------------- \\ \\ x=6 \\ \\ y=(9)/(2) \\ \\ z=10 \end{gathered}`

Therefore the x = 6 and y = 9/2 and z = 10 is the answer.