Let's find the cost per pound (because we are given average of cost per pound) of the 10 pound bag and 25 pound bag:
[tex] \frac{80}{10} = 8 [/tex]
[tex] \frac{150}{25} = 6 [/tex]
Since the average of the three bags is 6, we can set up an equation, where x is the cost per pound for the 50 pound bag:
[tex] \frac{8+6+x}{3} = 6 [/tex]
Solve:
[tex] 14+x=18 [/tex]
[tex] x = 4 [/tex]
Now, we have the cost per pound for the 50 pound bag, so let's multiply:
[tex] 50*4 = 200 [/tex]
All in all, the 50 lbs bag cost $200.
