Two machines

Performances of two machines are in a ratio of 7:12. A machine with less power produced 406 pieces of products per shift.

a) How many pieces produced per shift second machine?
b) How many pieces produced two machines together for five shifts?

Result

a =  696
b =  5510

Solution:

$7/(12+7) x=406 \ \\ x=406/7 \cdot \ (12+7)=1102 \ \\ a=12/(7+12) \cdot \ x=12/(7+12) \cdot \ 1102=696$
$b=5 \cdot \ (a + 406)=5 \cdot \ (696 + 406)=5510$

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