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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. )

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 class=

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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:

[tex]\begin{gathered} x+y+z=9 \\ \\ \\ \\ \frac{1}{2}x=\frac{4}{2}=2 \\ \\ \frac{1}{4}y=\frac{6}{4}=\frac{3}{2} \\ \\ \frac{1}{3}z=\frac{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(\frac{3}{2})+3(\frac{10}{3})=6+\frac{9}{2}+10 \\ \\ \\ \text{Therefore:} \\ \\ ------------------------------- \\ \\ x=6 \\ \\ y=\frac{9}{2} \\ \\ z=10 \end{gathered}[/tex]

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