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Answer :
We are given the system of inequalities representing the available resources:
[tex]$$
17T + 6C \leq 150 \quad \text{(wooden boards)}
$$[/tex]
[tex]$$
34T + 27C \leq 330 \quad \text{(nails)}
$$[/tex]
Fleur wants to make [tex]$3$[/tex] tables and [tex]$9$[/tex] chairs. We will substitute [tex]$T = 3$[/tex] and [tex]$C = 9$[/tex] into the expressions for the resources used.
1. Calculate the number of wooden boards needed:
[tex]$$
17T + 6C = 17(3) + 6(9) = 51 + 54 = 105.
$$[/tex]
Since [tex]$105 \leq 150$[/tex], she has enough wooden boards.
2. Calculate the number of nails needed:
[tex]$$
34T + 27C = 34(3) + 27(9) = 102 + 243 = 345.
$$[/tex]
Since [tex]$345 \not\leq 330$[/tex] (in fact, [tex]$345 > 330$[/tex]), she does not have enough nails.
Therefore, even though Fleur has enough wooden boards, she does not have enough nails to make [tex]$3$[/tex] tables and [tex]$9$[/tex] chairs.
The correct answer is:
(B) Fleur has enough boards but not enough nails.
[tex]$$
17T + 6C \leq 150 \quad \text{(wooden boards)}
$$[/tex]
[tex]$$
34T + 27C \leq 330 \quad \text{(nails)}
$$[/tex]
Fleur wants to make [tex]$3$[/tex] tables and [tex]$9$[/tex] chairs. We will substitute [tex]$T = 3$[/tex] and [tex]$C = 9$[/tex] into the expressions for the resources used.
1. Calculate the number of wooden boards needed:
[tex]$$
17T + 6C = 17(3) + 6(9) = 51 + 54 = 105.
$$[/tex]
Since [tex]$105 \leq 150$[/tex], she has enough wooden boards.
2. Calculate the number of nails needed:
[tex]$$
34T + 27C = 34(3) + 27(9) = 102 + 243 = 345.
$$[/tex]
Since [tex]$345 \not\leq 330$[/tex] (in fact, [tex]$345 > 330$[/tex]), she does not have enough nails.
Therefore, even though Fleur has enough wooden boards, she does not have enough nails to make [tex]$3$[/tex] tables and [tex]$9$[/tex] chairs.
The correct answer is:
(B) Fleur has enough boards but not enough nails.
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