$\begin{array}{r} 17 T+6 C \leq 150 \\ 34 T+27 C \leq 330 \end{array}$ $\newline$ Fleur wants to make tables and chairs. Each chair or table is made with the same number of wooden boards and nails. She has a total of $150$ wooden boards and $330$ nails. The system of inequalities shown represents the number of tables $(T)$ and chairs $(C)$ she can make in this situation. 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.

View step-by-step help

Home

Math Problems

Algebra 1

Interpret parts of quadratic expressions: word problems

Full solution

\begin{array}{r} 17 T+6 C \leq 150 \\ 34 T+27 C \leq 330 \end{array}

\newline

Fleur wants to make tables and chairs. Each chair or table is made with the same number of wooden boards and nails. She has a total of

150

wooden boards and

330

nails. The system of inequalities shown represents the number of tables

(T)

and chairs

(C)

she can make in this situation. 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

\newline

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

Check Wooden Boards: Determine if Fleur has enough wooden boards to make $3$ tables and $9$ chairs. $\newline$ The inequality for wooden boards is $17T + 6C \leq 150$ . $\newline$ Substitute $T$ with $3$ and $C$ with $9$ . $\newline$ $17(3) + 6(9) \leq 150$ $\newline$ $51 + 54 \leq 150$ $\newline$ $105 \leq 150$
Check Nails: Check if the calculation in Step $1$ is correct and if it satisfies the inequality. $\newline$ $105$ is indeed less than or equal to $150$ , which means Fleur has enough wooden boards to make $3$ tables and $9$ chairs.
Check Nails: Check if the calculation in Step $1$ is correct and if it satisfies the inequality. $\newline$ $105$ is indeed less than or equal to $150$ , which means Fleur has enough wooden boards to make $3$ tables and $9$ chairs.Determine if Fleur has enough nails to make $3$ tables and $9$ chairs. $\newline$ The inequality for nails is $34T + 27C \leq 330$ . $\newline$ Substitute $T$ with $3$ and $C$ with $9$ . $\newline$ $150$ $1$ $\newline$ $150$ $2$ $\newline$ $150$ $3$
Check Nails: Check if the calculation in Step $1$ is correct and if it satisfies the inequality. $\newline$ $105$ is indeed less than or equal to $150$ , which means Fleur has enough wooden boards to make $3$ tables and $9$ chairs.Determine if Fleur has enough nails to make $3$ tables and $9$ chairs. $\newline$ The inequality for nails is $34T + 27C \leq 330$ . $\newline$ Substitute $T$ with $3$ and $C$ with $9$ . $\newline$ $150$ $1$ $\newline$ $150$ $2$ $\newline$ $150$ $3$ Check if the calculation in Step $3$ is correct and if it satisfies the inequality. $\newline$ $150$ $4$ is not less than or equal to $150$ $5$ , which means Fleur does not have enough nails to make $3$ tables and $9$ chairs.