# Nine batteries are hooked in series to provide a 33-V power source. Some of the batteries are 3 V and some are 4.5 V. How many of each type are used?

Question
Equations and inequalities
Nine batteries are hooked in series to provide a 33-V power source. Some of the batteries are 3 V and some are 4.5 V. How many of each type are used?

2021-03-09
There is a total of 9 batteries: x+y=9
Since the batteries are in series, the total amount of voltage 33V is the sum of the individual voltages of the batteries: 3x+4.5y=33
Solve for y using (1) to obtain (3): y=9-x
Substitute (3) to (2) and solve for x: 3x+4.5(9-x)=33
3x+40.5-4.5x=33
-1.5x+40.5=33
-1.5x=-7.5
x=5
Solve for y using (3): y=9-5
y=4
So, there were 5 3V batteries and 4 4.5V batteries.

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b. Describe what new forwarding paths are needed for the rearranged pipeline by stating the source, destination, and information transferred on each needed new path.
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Method $$B: 0.36, 1.35, 2.56, 3.92, 5.35, 8.33, 10.70, 10.91$$