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Fleur wants to make tables and chairs. She has a total of 150150 wooden boards and 330330 nails.\newline17T+6C15017T+6C \leq 150 represents the number of tables TT and chairs CC she can make with 150150 wooden boards.\newline34T+27C33034T+27C \leq 330 represents the number of tables and chairs she can make with 330330 nails.\newlineDoes Fleur have enough boards and nails to make 33 tables and 99 chairs?\newlineChoose 11 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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Q. Fleur wants to make tables and chairs. She has a total of 150150 wooden boards and 330330 nails.\newline17T+6C15017T+6C \leq 150 represents the number of tables TT and chairs CC she can make with 150150 wooden boards.\newline34T+27C33034T+27C \leq 330 represents the number of tables and chairs she can make with 330330 nails.\newlineDoes Fleur have enough boards and nails to make 33 tables and 99 chairs?\newlineChoose 11 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.
  1. Calculate Boards Needed: Calculate the number of wooden boards needed for 33 tables and 99 chairs using the equation 17T+6C15017T + 6C \leq 150. Substituting T=3T = 3 and C=9C = 9, we get 17(3)+6(9)=51+54=10517(3) + 6(9) = 51 + 54 = 105.
  2. Check Board Availability: Check if 105105 boards is less than or equal to 150150 boards available. Since 105150105 \leq 150, Fleur has enough boards.
  3. Calculate Nails Needed: Calculate the number of nails needed for 33 tables and 99 chairs using the equation 34T+27C33034T + 27C \leq 330. Substituting T=3T = 3 and C=9C = 9, we get 34(3)+27(9)=102+243=34534(3) + 27(9) = 102 + 243 = 345.
  4. Check Nail Availability: Check if 345345 nails is less than or equal to 330330 nails available. Since 345>330345 > 330, Fleur does not have enough nails.