Workshop production

Five hundred ninety pieces of clothing were to be sewn in the two branches of the tailor's workshop. However, 30% more were sewn in the first workshop and 10% more in the second. They sewed a total of 703 pieces. How many products were initially supposed to be sewn by the first branch?

Final Answer:

a =  270

Step-by-step explanation:

$$\begin{gathered} a+b=590 \\ 1.30a+1.10b=703 \\ 1.30\cdot a+1.10\cdot b=703 \\ a+b=590 \\ 1.3a+1.1b=703 \\ Pivot:Row1\leftrightarrow Row2 \\ Row2-\frac{1}{1.3}\cdot Row1\to Row2 \\ 0.15b=49.23 \\ b=\frac{49.23076923}{0.15384615}=320 \\ a=\frac{703-1.1b}{1.3}=\frac{703-1.1\cdot 320}{1.3}=270 \\ a=270 \\ b=320 \end{gathered}$$

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