A company manufactures two types of cabinets, type 1 and type 2. It produces 110 total cabinets each week.
Last week, the number of type 2 cabinets produced exceeded twice the number of type 1 cabinets produced by 20. If x is the number of type 1 cabinets produced and y is the number of type 2 cabinets produced, the system of equations that represents this situation is x + y = 110 and y = 2x + 20.
The number of type 2 cabinets produced last week is
. This number exceeds the number of type 1 cabinets produced during the week by
.
The number of type 2 cabinets produced last week is y=2x+20
Substituting this into the equation x + y = 110:
x + (2x + 20) = 110
Combining like terms:
3x + 20 = 110
Subtracting 20 from both sides:
3x = 90
Dividing by 3:
x = 30
So the number of type 1 cabinets produced last week is x = 30.
Substituting this value back into the equation y = 2x + 20:
y = 2(30) + 20
y = 60 + 20
y = 80
Therefore, the number of type 2 cabinets produced last week is 80. This number exceeds the number of type 1 cabinets produced during the week by 80 - 30 = 50. Answer: \boxed{50}.