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
ANSWERED
asked 2021-05-28
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.

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