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Pierre wants to make tables and chairs. He has a total of 220 wooden boards and 760 nails. 13 T+8C <= 220 represents the number of tables T and chairs C he can make with 220 wooden boards. 48 T+37 C <= 760 represents the number of tables and chairs he can make with 760 nails. Does Pierre have enough boards and nails to make 9 tables and 5 chairs? Choose 1 answer: (A) Pierre has enough boards and nails. (B) Pierre has enough boards but not enough nails. (c) Pierre has enough nails but not enough boards. (D) Pierre has neither enough boards nor enough nails.

Pierre wants to make tables and chairs. He has a total of 220220 wooden boards and 760760 nails.\newline13T+8C≤22013T+8C \leq 220 represents the number of tables TT and chairs CC he can make with 220220 wooden boards.\newline48T+37C≤76048T+37C \leq 760 represents the number of tables and chairs he can make with 760760 nails.\newlineDoes Pierre have enough boards and nails to make 99 tables and 55 chairs?\newlineChoose 11 answer:\newline(A) Pierre has enough boards and nails.\newline(B) Pierre has enough boards but not enough nails.\newline(C) Pierre has enough nails but not enough boards.\newline(D) Pierre has neither enough boards nor enough nails.

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Q. Pierre wants to make tables and chairs. He has a total of 220220 wooden boards and 760760 nails.\newline13T+8C≤22013T+8C \leq 220 represents the number of tables TT and chairs CC he can make with 220220 wooden boards.\newline48T+37C≤76048T+37C \leq 760 represents the number of tables and chairs he can make with 760760 nails.\newlineDoes Pierre have enough boards and nails to make 99 tables and 55 chairs?\newlineChoose 11 answer:\newline(A) Pierre has enough boards and nails.\newline(B) Pierre has enough boards but not enough nails.\newline(C) Pierre has enough nails but not enough boards.\newline(D) Pierre has neither enough boards nor enough nails.
  1. Identify Constraints for Boards: Identify the constraints for the wooden boards.\newlineThe inequality 13T+8C≤22013T + 8C \leq 220 represents the maximum number of tables (T)(T) and chairs (C)(C) Pierre can make with the wooden boards he has.
  2. Check Boards Availability: Substitute the values of TT and CC into the wooden boards inequality to check if Pierre has enough boards to make 99 tables and 55 chairs.\newlineFor T=9T = 9 and C=5C = 5, the inequality becomes 13(9)+8(5)≤22013(9) + 8(5) \leq 220.\newlineCalculate the left side of the inequality: 13×9+8×5=117+40=15713 \times 9 + 8 \times 5 = 117 + 40 = 157.
  3. Compare Boards Quantity: Compare the calculated value with the number of boards available.\newlineSince 157≤220157 \leq 220, Pierre has enough wooden boards to make 99 tables and 55 chairs.
  4. Identify Constraints for Nails: Identify the constraints for the nails. The inequality 48T+37C≤76048T + 37C \leq 760 represents the maximum number of tables (TT) and chairs (CC) Pierre can make with the nails he has.
  5. Check Nails Availability: Substitute the values of TT and CC into the nails inequality to check if Pierre has enough nails to make 99 tables and 55 chairs.\newlineFor T=9T = 9 and C=5C = 5, the inequality becomes 48(9)+37(5)≤76048(9) + 37(5) \leq 760.\newlineCalculate the left side of the inequality: 48×9+37×5=432+185=61748 \times 9 + 37 \times 5 = 432 + 185 = 617.
  6. Compare Nails Quantity: Compare the calculated value with the number of nails available.\newlineSince 617≤760617 \leq 760, Pierre has enough nails to make 99 tables and 55 chairs.
  7. Verify Resource Sufficiency: Determine if Pierre has enough resources to make 99 tables and 55 chairs.\newlineSince Pierre has enough wooden boards and enough nails, he can make 99 tables and 55 chairs.

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