Judith McQueen

Answered

2021-12-16

Suppose that factory A produces 12 tables and 6 chairs an hour while factory B produces 8 tables and 4 chairs an hour. How many hours should each factory work to produce 48 tables and 24 chairs? How many different solutions are there to this problem?

Answer & Explanation

puhnut1m

Expert

2021-12-17Added 33 answers

Let factory A works for x hours

factory B works for y hours

According to the question$12x+8y=48$

$6x+4y=24$

$\frac{12}{6}=\frac{8}{4}=\frac{48}{24}$

$\frac{2}{1}=\frac{2}{1}=\frac{2}{1}$

They are same equations

There are finite solution possible for this equation

$6x+4y=2$

$\Rightarrow 3x+2y=12$

$$\begin{array}{|cc|}\hline x& y\\ 0& 6\\ 2& 3\\ 4& 0\\ \hline\end{array}$$

$x\ge 0$

$y\ge 0$

Three different solution is possible

$x=0\text{}x=2\text{}x=4$

$y=6\text{}y=3\text{}y=0$

factory B works for y hours

According to the question

They are same equations

There are finite solution possible for this equation

Three different solution is possible

zesponderyd

Expert

2021-12-18Added 42 answers

You actually wont

RizerMix

Expert

2021-12-29Added 437 answers

A.

NSK

B.

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