Individually 65314

A bakery worker makes 300 rolls more than an apprentice in 2 hours. In 4 hours, they both made 9800 rolls together. What are the hourly output of the worker and the apprentice individually?

Correct answer:

a =  1300
b =  1150

Step-by-step explanation:

$$\begin{gathered} 2a=300+2b \\ 4a+4b=9800 \\ 2\cdot a=300+2\cdot b \\ 4\cdot a+4\cdot b=9800 \\ 2a-2b=300 \\ 4a+4b=9800 \\ Pivot:Row1\leftrightarrow Row2 \\ 4a+4b=9800 \\ 2a-2b=300 \\ Row2-\frac{2}{4}\cdot Row1\to Row2 \\ 4a+4b=9800 \\ -4b=-4600 \\ b=\frac{-4600}{-4}=1150 \\ a=\frac{9800-4b}{4}=\frac{9800-4\cdot 1150}{4}=1300 \\ a=1300 \\ b=1150 \end{gathered}$$

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