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A group of ten
6- and 12-volt batteries are
wired in series as shown at
the right.The sum of their
voltages is 84 volts.How
many of each type of
battery are used?I need an equasion

2006-10-05 11:40:17 · 8 answers · asked by techline210 2 in Science & Mathematics Mathematics

8 answers

(1) 6x + 12y = 84
(2) x + y = 10

(3) y = 10 - x

6x + 12(10 - x) = 84

6x + 120 - 12x = 84

-6x = -36

x = 6

x + y = 10

6 + y = 10

y = 4

This means that there are six 6V batteries, and four 12V batteries

2006-10-05 11:49:32 · answer #1 · answered by عبد الله (ドラゴン) 5 · 0 0

Step 1. Set up the problem as a system of simultaneous equations.

First equation:
6a + 12b = 84

Second equation:
a + b = 10

Step 2. Multiply the 2nd equation by six on both sides.
6(a + b) = 6(10)
6a + 6b = 60

Step 3. Subtract the amended 2nd equation in Step 2 from the 1st equation.
6a + 12b - (6a + 6b) = 84 - 60
6a - 6a + 12b - 6b = 24
6b = 24

Step 4. Find b, the number of 12-volt batteries.
b = 24 / 6
b = 4

Step 5. Find a, the number of 6-volt batteries.
a + b = 10
b = 4
a = 10 - 4
a = 6

Check:
6(6) + 12(4) = 36+48 = 84

2006-10-05 11:43:55 · answer #2 · answered by David S 5 · 0 0

12x+6(10-x)=84
12x+60-6x=84
6x=24
x=4 12 volt batteries
10-4=6 6 volt batteries
check
4*12+6*6=48+36=84

2006-10-09 09:35:39 · answer #3 · answered by yupchagee 7 · 0 0

let x = 6 volt batteries and y = 12 volt batteries

x + y = 10
6x + 12 y = 84

then solve the first for x, and substitute in from there!

2006-10-05 11:44:47 · answer #4 · answered by emma 1 · 0 0

Let x=number of 6 volt batteries
Let y=number of 12 volt batteries
6x+12y=84
x+y=10
solve for x
x=10-y
substitute
6(10-y)+12y=84
60-6y+12y=84
60+6y=84
6y=24
y=4
substitute again
x+4=10
x=6
Now check your work
6(6)+12(4)=84
36+48=84
True
6 six volt batteries.
4 twelve volt batteries.

2006-10-05 11:51:06 · answer #5 · answered by David 3 · 0 0

6(N) + 12(10-N) =84

solve for N. Thats the number of 6v batteries

2006-10-05 11:44:46 · answer #6 · answered by davidosterberg1 6 · 0 0

6 volt = v
12 volt = (2v)

10[v+(2v)] = 84


four 12 volt and six 6 volt

2006-10-05 11:47:43 · answer #7 · answered by Nikitty 2 · 0 0

where's the diagram?

2006-10-05 11:42:06 · answer #8 · answered by Anonymous · 0 0

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