Question

# A glue company needs to make some glue that it can sell at $120 per barrel. It wants to use 150 barrels of glue worth$100 per barrel, along with some

Probability and combinatorics
A glue company needs to make some glue that it can sell at $120 per barrel. It wants to use 150 barrels of glue worth$100 per barrel, along with some glue worth $150 per barrel and glue worth$190 per barrel. It must use the same number of barrels of $150 and$190 glue. How much of the $150 and$190 glue will be needed? How many barrels of $120 glue will be produced? ## Expert Answers (1) 2021-05-29 Let x-> number of barrels of glue worth$150 per barrel
y-> number of barrels of glue worth $190 per barrel The glue must sell for$120 per barrel so: $$100(150)+150x+190y=120(150+x+y)$$
It must use the same number of barrels of $150 and$190 glue: x=y
Substitute (2) to (1) and solve for x: $$100(150)+150x+190x=120(150+x+x)$$
$$15000+340x=18000+240x$$
$$15000+100x=18000$$
$$100x=3000$$
$$x=30$$
which follows that: $$y=30$$
So, the company will need 30 barrels of the $150 and$190 glue. The number of barrels to be used is $$150+x+y=150+30+30=210$$ barrels.