Question 159558: Ten 6.0-V and 12-V batteries have a total voltage of 84 V.How many of each type are there ??? Found 2 solutions by KnightOwlTutor, gonzo:Answer by KnightOwlTutor(293) (Show Source):
X=# of 6.0 Volt batteries
10-X=3 0f 12 Volt batteries
#of batteriesX individual voltage =total voltage amount
The equation is
6(X)+12(10-X)=84
Use the distributive property
6X+120-12X=84
Subtract 120 from both sides
6X-12X=-36
Add the X terms
-6X=-36
X=6
Therefore you have 6 6 Volt batteries and 4 12V batteries
Double check bu plugging in values in the above expression
6(6)+12(4)=84
You can put this solution on YOUR website! total voltage is 84.
total number of batteries is 10.
let x = number of 6 volt batteries.
let y = number of 12 volt batteries.
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x + y = 10
6*x + 12*y = 84
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first equation provides number of batteries in total.
second equation provides number of volts in total.
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in the first equation you can solve for x or y. we'll solve for x.
subtract y from both sides of the equation.
equation becomes x = 10 - y.
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substitute (10 - y) for x in the second equation to remove one of the unknowns and equation becomes 6*(10-y) + 12*y = 84
which becomes 60 - 6*y + 12*y = 84
which becomes 60 + 6*y = 84
subtract 60 from both sides of the equation and it becomes 6*y = 84 - 60
which becomes 6*y = 24
divide both sides of the equation by 6 and it becomes y = (24/6)
which becomes y = 4
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substitute 4 for y in the first equation
it becomes x + 4 = 10
subtract 4 from both sides of the equation and it becomes x = 6
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answer appears to be
x = 6
y = 4
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substitute 6 for x and 4 for y in the first equation and it becomes 6 + 4 = 10 which becomes 10 = 10 meaning x and y look to be good values in the first equation. that's not enough though. they have to good values for both equations.
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substitute 6 for x and 4 for y in the second equation and it becomes 6*6 + 4*12 = 84 which becomes 36 + 48 = 84 which becomes 84 = 84 meaning x and y look to be good values in the second equation as well.
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answer is x = 6 and y = 4.
x represents the number of 6 volt batteries.
y represents the number of 12 volt batteries.
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