Hal makes tables and chairs. Each chair requires 4 ft. of oak and 3 ft. of pine, while each table requires 8 ft. of oak and 2 ft. of pine. Hal has 52 ft. of oak and 23 ft. of pine. How many chairs and tables can he build?
2007-02-12 16:53:44 · 4 answers · asked by soccerrules 1 in Science & Mathematics ➔ Mathematics
Let T = number of tables
Let C = number of chairs
Let O = feet of Oak
Let P = feet of pine
(C x ((4 x O)+(3 x P) )+(T x ((8 x O)+(2 x P)) = (52 x O) + (23 x P)
Transposing
O x(4C+8T) + P x (3C +2T) = (52 x O) + (23 x P)
Solving for O
4C+8T = 52 ..............Equation 1
Solving for P
3C+2T = 23
Multiply solution for P by 4 and we get
12C+8T=92 ................Equation 2
Subtract equation 1 from equation 2
12C + 8T - 4C - 8T = 92 - 52
8C = 40
C = 40/8 = 5
Substituting C into equation 1
4 x 5 + 8 x T = 52
20 + 8T =52
Subtract 20 from both sides
8T = 32
Divide both sides by 8
T = 4
Hal can make 5 chairs and 4 tables and use all of the wood.
2007-02-12 17:29:50 · answer #1 · answered by John B 4 · 0⤊ 0⤋
Maximum 7 chairs...or 6 table...but not both...
Highest possible number of furniture in total is 4 table 5 chairs...
2007-02-13 01:03:58 · answer #2 · answered by Anonymous · 0⤊ 0⤋
5 chairs and 4 tables
2007-02-12 17:10:56 · answer #3 · answered by answerING 6 · 0⤊ 0⤋
4 tables and 5 chairs
4*8 (oak) 32 4*2 (pine) 8
5*4 (oak) 20 5*3 (pine) 15
____ ____
52 23
2007-02-12 17:06:16 · answer #4 · answered by momofspecialneeds 2 · 1⤊ 0⤋
thinking
2007-02-12 17:00:22 · answer #5 · answered by Anonymous · 0⤊ 0⤋