Particular 7338

Two workshops of a particular company produced 25 parts a day. To have 300 pieces, one worked for ten days and the other for 15 days. How many parts did each workshop make per day?

Correct answer:

a =  15
b =  10

Step-by-step explanation:

$a+b = 25 \ \\ 300 = 10a+15b \ \\ \ \\ a+b = 25 \ \\ 300 = 10 \cdot \ a+15 \cdot \ b \ \\ \ \\ a+b = 25 \ \\ 10a+15b = 300 \ \\ \ \\ Pivot: Row 1 ↔ Row 2 \ \\ 10a+15b = 300 \ \\ a+b = 25 \ \\ \ \\ Row 2 - \dfrac{ 1 }{ 10 } \cdot \ Row 1 → Row 2 \ \\ 10a+15b = 300 \ \\ -0.5b = -5 \ \\ \ \\ b = \dfrac{ -5 }{ -0.5 } = 10 \ \\ a = \dfrac{ 300-15b }{ 10 } = \dfrac{ 300-15 \cdot \ 10 }{ 10 } = 15 \ \\ \ \\ a = 15 \ \\ b = 10$

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