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.