what is the systems of equations for these problems?

Question

1. each chair requires 4ft of oak & 3ft of pine, while each table requires 8 ft of oak and 2ft of pine. hal has 52ft of oak and 23ft of pine how many chairs & tables can he build?

2. Sherdans monthly bill includes a fixed charge, which is the same eac month and an additional charge for toll calls. One month the bill was $22, which included charges for 5 toll calls. the following month the bill was $26, which included charges for 7 toll calls. find the fixed charge and the average charge per toll call

Answer 1

Hi. They are in the English system format.

Answer 2

You need to translate these into algebraic equations. Look at each word problem and determine what each part of the problem is saying and write it down in mathematical terms. I will walk you through one problem, to give you an idea of how to do it, but you will have to try the other one yourself (so that you can learn and get good at this type of problem!).

Problem #1 -- Let X = oak, Y = pine

"Each chair requires 4 ft of oak and 3 ft of pine" -- rewrite this as:

1 CHAIR = 4x + 3y

"Each table requires 8 ft of oak and 2 ft of pine" -- rewrite this as:

1 TABLE = 8x + 2y

"Hal has 53 ft of oak and 23 ft of pine; how many chairs and tables can he build"

Well, this part is a little tricky because he can build either all chairs, or all tables, or a combination of chairs and tables. Let's look at each one individually:

All chairs:
1 CHAIR = 4x + 3y
HAL = 52x + 23y

For the oak, 52/4 = 13, for the pine 23/3 = 7.67, so the most Hal could make would be 7 chairs, using 7*(4x+3y) = 28x + 21y = 28 ft of oak + 21 ft of pine, with 24 ft of oak and 2 ft of pine leftover.

Similary, if he were to make all tables:

1 TABLE = 8x + 2y
HAL = 52x + 23y

For the oak, 52/8 = 6.5, for the pine 23/2 = 11.5, so the most Hal could make would be 6 tables, using 6*(8x+2y) = 48x + 12y = 48 ft of oak + 12 ft of pine, with 4 ft of oak and 11 ft of pine leftover.

The key would be to find out how to maximize the number of chairs and tables such that the least amount of unused wood is left over. You need to use calculus for this, but I'm not sure if your math class is calculus or not. If it's not, then any further work that I could do on this problem involving calculus would be meaningless to you and not helpful for your problem.

I hope this helped somewhat!

Answer 3

Problem 2
Simlutaneous Eqn Let C be toll call chages and F be fix charges
5C+F=22 (1)
7C+F=26 (2)

Solve simultaneously (2) - (1)
2C=4 Thus Sub C=2 into (1)
C=2 F=12

Answer 4

too many?