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 [tex]\( x \)[/tex] is the number of type 1 cabinets produced and [tex]\( y \)[/tex] is the number of type 2 cabinets produced, the system of equations that represents this situation is:

[tex]\[ x + y = 110 \][/tex]
[tex]\[ y = 2x + 20 \][/tex]

The number of type 2 cabinets produced last week is [tex]\( \square \)[/tex].

This number exceeds the number of type 1 cabinets produced during the week by [tex]\( \square \)[/tex].

Question

18-06-2024
Mathematics

Answered

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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 [tex]\( x \)[/tex] is the number of type 1 cabinets produced and [tex]\( y \)[/tex] is the number of type 2 cabinets produced, the system of equations that represents this situation is:

[tex]\[ x + y = 110 \][/tex]
[tex]\[ y = 2x + 20 \][/tex]

The number of type 2 cabinets produced last week is [tex]\( \square \)[/tex].

This number exceeds the number of type 1 cabinets produced during the week by [tex]\( \square \)[/tex].

Sagot :

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GinnyAnsweridn GinnyAnsweridn · Answer 1 · 2024-06-18T14:51:54-04:00

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].

Sagot :

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