Two workshops

Two workshops were supposed to produce 4,000 sets of kitchen utensils together. After completing the task, it was found that the first workshop produced 534 sets more than originally planned for it, while the second workshop fulfilled its plan at 80%. How many sets of utensils did each workshop produce?

Final Answer:

a =  1864
b =  2136

Step-by-step explanation:

$$\begin{gathered} A+B=4000(plan) \\ a+b=4000 \\ a=534+A \\ b=0.80B \\ A+B=4000 \\ (534+A)+(0.80\cdot B)=4000 \\ A+0.8B=3466 \\ Row2-Row1\to Row2 \\ -0.2B=-534 \\ B=\frac{-534}{-0.2}=2670 \\ A=4000-B=4000-2670=1330 \\ A=1330 \\ B=2670 \\ a=534+A=534+1330=1864 \end{gathered}$$

$b=0.80\cdot B=0.80\cdot 2670=2136$

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