Judith McQueen

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?

puhnut1m

Expert

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
$6x+4y=2$
$⇒3x+2y=12$
$\begin{array}{|cc|}\hline x& y\\ 0& 6\\ 2& 3\\ 4& 0\\ \hline\end{array}$
$x\ge 0$
$y\ge 0$
Three different solution is possible

zesponderyd

Expert

You actually wont

RizerMix

Expert

A.  Factory A should work 4 hours.
NSK
B. Factory B should work 6 hours.

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