Question 100651
We have 10 batteries, so let's say the number of 6V batteries is x. That means the number of 12V batteries is 10 - x.

And we're told that 6x + 12(10-x) = 84 volts. 6x is the 6 volts per battery times x, which is the number of 6V batteries. Likewise 12(10-x) is the 12 volts per battery times the number of 12V batteries. 

So, we have 6x + 120 - 12x = 84. Combining the x terms we have -6x + 120 = 84. Subtracting 120 from both sides, we have -6x = -36. Dividing by -6, we have x = 6.

That means the number of 6V batteries is 6, and the number of 12V batteries is 10-6=4.

ALWAYS check! 6*6=36 and 4*12=48, 36+48=84. Check.