Pierre wants to make tables and chairs. he has a total of 220220 wooden boards and 760760 nails. 13 t+8 c \leq 22013t+8c≤220 represents the number of tables tt and chairs cc he can make with 220220 wooden boards. 48 t+37 c \leq 76048t+37c≤760 represents the number of tables and chairs he can make with 760760 nails.

Solution:

Number of wooden boards that Pierre possess= 220

Number of nails that Pierre have= 760

The two expression which represents the number of tables T and chairs C he can make with 220 wooden boards and 760 nails

1. 13 T+8 C≤220

2. 48 T+37 C≤760

We can solve it by two methods, either graphically or by finding their point of intersections,as these two are inequalities in two variable

Equation (1) × 37 - Equation (2) × 8

481 T + 296 C-384 T -296 C≤8140 - 6080

97 T ≤ 2060

T ≤ 21.23(approx)

Putting the value of T in equation (1),

13 × 21.23 + 8 C ≤ 220

347.80 + 8 C≤220

8 C ≤ 220 - 347.80

8 C≤-127.80

As, the value of Chairs (C) can't be negative.

So, the two inequalities which represents number of chairs and number of tables is incorrect.

So, we can't find total number of chairs and total number of tables with the given inequalities.

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

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

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

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

Step-by-step explanation:

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

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

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.