An order of 12 dozen rollerball pens and 5 dozen ballpoint pens cost $116. a later order 8 dozen rollerball pens and 12 dozen ballpoint pens cost $112. what was the cost of 1 dozen of pens? and how much does 1 dozen pencils cost?

R=cost per dozen rollerball pens
b=cost per dozen ballpoint pens
p=cost per dozen pencils
???

ignore pencils

12r+5b=116
8r+12b=112

eliminate
simplify last equation by dividing by 4
2r+3b=28

eliminate r's
multiply 2r+3b=28 by -6 and add to top equation

-12r-18b=-168
12r+5b=116 +
0r-13b=-52

-13b=-52
divide both sides by -13
b=4

plug back in
2r+3b=28
2r+3(4)=28
2r+12=28
minus 12
2r=16
divide by 2
r=8

ballpoint=pencils

1dozen pencils=$4
1dozen rollerbladepens=$8