SOLUTION: Three batteries are connected in series so that the total voltage is 54 volts. The voltage of the first battery is twice the voltage of the second and 1/3 the voltage of the third

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Question 437868: Three batteries are connected in series so that the total voltage is 54 volts. The voltage of the first battery is twice the voltage of the second and 1/3 the voltage of the third battery. Find the actual voltage of each battery.

Found 2 solutions by josmiceli, Gogonati:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let b = voltage of 2nd battery
2b = voltage the 1st battery
+3%2A%282b%29+=+6b+ = voltage of 3rd battery
+b+%2B+2b+%2B+6b+=+54+
+9b+=+54+
+b+=+6+
+2b+=+12+
+6b+=+36+
The batteries are
6v, 12v, and 36v

Answer by Gogonati(855) About Me  (Show Source):
You can put this solution on YOUR website!
Since the batteries are connected in series the total voltage is equal to the sum of voltages connected in series:
U=U%5B1%5D%2BU%5B2%5D%2BU%5B3%5D
Let U%5B3%5D=x volt the voltage of third battery then the voltage of the first
is U%5B1%5D=%282%2F3%29%2Ax and the voltage of the second is U%5B2%5D=%281%2F3%29%2Ax
Substitute and have:54=%282%2F3%29x%2B%281%2F3%29x%2Bx, solve this equation:
54=2x => x=27
Answer: The third battery is 27 v, the second is %281%2F3%29%2A27=9v and
the first is %282%2F3%29%2A27=18v