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Answer :
To determine whether Fleur has enough boards and nails to make 3 tables and 9 chairs, we need to compare her resources to the constraints given by the system of inequalities:
1. Boards Constraint: [tex]\(17T + 6C \leq 150\)[/tex]
- For 3 tables ([tex]\(T = 3\)[/tex]) and 9 chairs ([tex]\(C = 9\)[/tex]), calculate the number of boards used:
[tex]\[
17 \times 3 + 6 \times 9 = 51 + 54 = 105
\][/tex]
- Check if this is within the limit:
[tex]\[
105 \leq 150
\][/tex]
This condition is true, so Fleur has enough boards.
2. Nails Constraint: [tex]\(34T + 27C \leq 330\)[/tex]
- Again for 3 tables ([tex]\(T = 3\)[/tex]) and 9 chairs ([tex]\(C = 9\)[/tex]), calculate the number of nails used:
[tex]\[
34 \times 3 + 27 \times 9 = 102 + 243 = 345
\][/tex]
- Check if this is within the limit:
[tex]\[
345 \leq 330
\][/tex]
This condition is false, meaning Fleur does not have enough nails.
Since the nail constraint is not satisfied, Fleur does not have enough resources to make 3 tables and 9 chairs.
1. Boards Constraint: [tex]\(17T + 6C \leq 150\)[/tex]
- For 3 tables ([tex]\(T = 3\)[/tex]) and 9 chairs ([tex]\(C = 9\)[/tex]), calculate the number of boards used:
[tex]\[
17 \times 3 + 6 \times 9 = 51 + 54 = 105
\][/tex]
- Check if this is within the limit:
[tex]\[
105 \leq 150
\][/tex]
This condition is true, so Fleur has enough boards.
2. Nails Constraint: [tex]\(34T + 27C \leq 330\)[/tex]
- Again for 3 tables ([tex]\(T = 3\)[/tex]) and 9 chairs ([tex]\(C = 9\)[/tex]), calculate the number of nails used:
[tex]\[
34 \times 3 + 27 \times 9 = 102 + 243 = 345
\][/tex]
- Check if this is within the limit:
[tex]\[
345 \leq 330
\][/tex]
This condition is false, meaning Fleur does not have enough nails.
Since the nail constraint is not satisfied, Fleur does not have enough resources to make 3 tables and 9 chairs.
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