Question 221190
A group of ten 6- and 12-volt batteries are wired in series.   The sum of their voltages produces a power supply of 84 volts.  How many of each type battery are used?


Step 1.  Let x be the number of 6-volt batteries.


Step 2.  Let 10-x be the number of 12-volt batteries.


Step 3.  Batteries are connected in series, so 6x is the total voltage from 6-volt batteries and 12(10-x) is the total voltage from 12-volt batteries.


Step 4.  Then {{{6x+12(10-x)=84}}} since the sum of their voltages is 84 volts.


Step 5.  Simplifying the equation in Step 4.


{{{6x+120-12x=84}}}


{{{-6x+120=84}}}


Add 6x-84 to both sides of the equation


{{{-6x+120+6x-84=84+6x-84}}}



{{{36=6x}}}


Divide by 6 to both sides of the equation


{{{36/6=4x/6}}}


{{{x=6}}} and {{{10-x=4}}}


Check total voltage...{{{6*6+4*12=36+48=84}}}  which is a true statement.


Step 6:  ANSWER: There are six 6-volt batteries and four 12-volt batteries.


I hope the above steps and explanation were helpful. 


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Respectfully, 
Dr J