SOLUTION: 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?

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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?
Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
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%2B12%2810-x%29=84 since the sum of their voltages is 84 volts.

Step 5. Simplifying the equation in Step 4.

6x%2B120-12x=84

-6x%2B120=84

Add 6x-84 to both sides of the equation

-6x%2B120%2B6x-84=84%2B6x-84


36=6x

Divide by 6 to both sides of the equation

36%2F6=4x%2F6

x=6 and 10-x=4

Check total voltage...6%2A6%2B4%2A12=36%2B48=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.

For Step-By-Step videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry please visit http://www.FreedomUniversity.TV/courses/Trigonometry.

Also, good luck in your studies and contact me at john@e-liteworks.com for your future math needs.

Respectfully,
Dr J