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

17 T+6C <= 150 represents the number of tables
T and chairs
C she can make with 150 wooden boards.

34 T+27 C <= 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 1 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.

Fleur wants to make tables and chairs. She has a total of $150$ wooden boards and $330$ nails. $\newline$ $17T+6C \leq 150$ represents the number of tables $T$ and chairs $C$ she can make with $150$ wooden boards. $\newline$ $34T+27C \leq 330$ represents the number of tables and chairs she can make with $330$ nails. $\newline$ Does Fleur have enough boards and nails to make $3$ tables and $9$ chairs? $\newline$ Choose $1$ answer: $\newline$ (A) Fleur has enough boards and nails. $\newline$ (B) Fleur has enough boards but not enough nails. $\newline$ (C) Fleur has enough nails but not enough boards. $\newline$ (D) Fleur has neither enough boards nor enough nails.

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Modeling with linear inequalities

Full solution

Q. Fleur wants to make tables and chairs. She has a total of

150

wooden boards and

330

nails.

\newline

17T+6C \leq 150

represents the number of tables

T

and chairs

C

she can make with

150

wooden boards.

\newline

34T+27C \leq 330

represents the number of tables and chairs she can make with

330

nails.

\newline

Does Fleur have enough boards and nails to make

3

tables and

9

chairs?

\newline

Choose

1

answer:

\newline

(A) Fleur has enough boards and nails.

\newline

(B) Fleur has enough boards but not enough nails.

\newline

(C) Fleur has enough nails but not enough boards.

\newline

(D) Fleur has neither enough boards nor enough nails.

Check wooden board availability: Check if Fleur has enough wooden boards to make $3$ tables and $9$ chairs using the inequality $17T + 6C \leq 150$ . $\newline$ Substitute $T$ with $3$ and $C$ with $9$ . $\newline$ $17(3) + 6(9) \leq 150$ $\newline$ $51 + 54 \leq 150$ $\newline$ $105 \leq 150$
Verify wooden board calculation: Verify the calculation for the number of wooden boards needed. $\newline$ $51 + 54 = 105$ $\newline$ $105 \leq 150$ is a true statement, which means Fleur has enough wooden boards to make $3$ tables and $9$ chairs.
Check nail availability: Check if Fleur has enough nails to make $3$ tables and $9$ chairs using the inequality $34T + 27C \leq 330$ . $\newline$ Substitute $T$ with $3$ and $C$ with $9$ . $\newline$ $34(3) + 27(9) \leq 330$ $\newline$ $102 + 243 \leq 330$ $\newline$ $345 \leq 330$
Verify nail calculation: Verify the calculation for the number of nails needed. $\newline$ $102 + 243 = 345$ $\newline$ $345 \leq 330$ is a false statement, which means Fleur does not have enough nails to make $3$ tables and $9$ chairs.

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