Middle School

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Fleur wants to make tables and chairs. She has a total of 150 wooden boards and 330 nails.

The inequality \(17T + 6C \leq 150\) represents the number of tables \(T\) and chairs \(C\) she can make with 150 wooden boards.

The inequality \(34T + 27C \leq 330\) represents the number of tables and chairs she can make with 330 nails.

Does Fleur have enough boards and nails to make 3 tables and 9 chairs?

Choose one answer:

A. Fleur has enough boards and nails.
B. Fleur has enough boards but not enough nails.
C. Fleur has enough nails but not enough boards.
D. Fleur has neither enough boards nor enough nails.

Answer :

Answer::

Choice B : fleur has enough boards but not enough nails

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Rewritten by : Barada

Final answer:

To determine if Fleur has enough boards and nails to make 3 tables and 9 chairs, we substitute the values in the given inequalities and check if they hold true.

Explanation:

To determine if Fleur has enough boards and nails to make 3 tables and 9 chairs, we need to check if the given inequalities are satisfied. We can substitute T with 3 and C with 9 in the first inequality and check if it holds true. Similarly, we can substitute T with 3 and C with 9 in the second inequality and check if it holds true.

For the first inequality, 17(3) + 6(9) ≤ 150 simplifies to 51 + 54 ≤ 150, which is true. For the second inequality, 34(3) + 27(9) ≤ 330 simplifies to 102 + 243 ≤ 330, which is also true.

Since both inequalities are satisfied, Fleur has enough boards and nails to make 3 tables and 9 chairs. The answer is (Choice A) Fleur has enough boards and nails.

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