To solve the problem, we need to determine the number of type 1 cabinets ([tex]\(x\)[/tex]) and type 2 cabinets ([tex]\(y\)[/tex]) produced based on the given equations:
1. [tex]\(x + y = 110\)[/tex]
2. [tex]\(y = 2x + 20\)[/tex]
By solving this system of equations, we determine the values of [tex]\(x\)[/tex] and [tex]\(y\)[/tex]. The solutions to these equations are:
- [tex]\( x = 30 \)[/tex] (the number of type 1 cabinets produced)
- [tex]\( y = 80 \)[/tex] (the number of type 2 cabinets produced)
The first part of our answer is the number of type 2 cabinets produced, which is [tex]\(80\)[/tex].
Next, we need to find by how much the number of type 2 cabinets produced exceeds the number of type 1 cabinets produced. We do this by subtracting the number of type 1 cabinets from the number of type 2 cabinets:
[tex]\[ y - x = 80 - 30 = 50 \][/tex]
Therefore, the number of type 2 cabinets produced exceeds the number of type 1 cabinets by [tex]\(50\)[/tex].
Thus, the complete answers are:
- The number of type 2 cabinets produced last week is [tex]\(80\)[/tex].
- This number exceeds the number of type 1 cabinets produced during the week by [tex]\(50\)[/tex].
