Pierre wants to make tables and chairs. He has a total of 220 wooden boards and 760 nails. 13T+8C≤220 represents the number of tables T and chairs C he can make with 220 wooden boards. 48T+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?

Question

Mathematics

Seth Horn

1 June, 21:30

Pierre wants to make tables and chairs. He has a total of 220 wooden boards and 760 nails. 13T+8C≤220 represents the number of tables T and chairs C he can make with 220 wooden boards. 48T+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?

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Answers (1)

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Ethan Long · Answer 1

Pierre has enough boards and nails to make 9 tables and 5 chairs.

Step-by-step explanation:

13T+8C ≤ 220

Let us substitute 9 for T and 5 for C and check.

13 (9) + 8 (5) = 117 + 40

= 157 < 220

So, 220 wooden boards are sufficient to make 9 tables and 5 chairs.

48T+37C ≤ 760

Substitute 9 for T and 5 for C.

48 (9) + 37 (5) = 432 + 185

= 617 < 760

So, 760 nails are sufficient to make 9 tables and 5 chairs.

Hence, Pierre has enough boards and nails to make 9 tables and 5 chairs.