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A company manufactures two types of cabinets, Type 1 and Type 2. It produces 110 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 :

GinnyAnswer
To find the number of type 2 cabinets produced last week and by how much this number exceeds the number of type 1 cabinets produced, we can solve the system of equations step by step.

Given:
1. [tex]\( x + y = 110 \)[/tex]
2. [tex]\( y = 2x + 20 \)[/tex]

First, let's solve for [tex]\( x \)[/tex]:

1. From equation [tex]\( x + y = 110 \)[/tex], we can express [tex]\( y \)[/tex] as:

[tex]\( y = 110 - x \)[/tex]

2. Set the expression for [tex]\( y \)[/tex] from the second equation equal to the expression for [tex]\( y \)[/tex] from the first equation:

[tex]\( 2x + 20 = 110 - x \)[/tex]

3. Combine like terms to solve for [tex]\( x \)[/tex]:

[tex]\( 3x = 90 \)[/tex]

4. Divide both sides by 3:

[tex]\( x = 30 \)[/tex]

Next, using the value of [tex]\( x \)[/tex] to find [tex]\( y \)[/tex]:

1. Substitute [tex]\( x = 30 \)[/tex] back into the second equation:

[tex]\( y = 2(30) + 20 \)[/tex]

2. Simplify:

[tex]\( y = 60 + 20 \)[/tex]

[tex]\( y = 80 \)[/tex]

Finally, we find how much the number of type 2 cabinets exceeds the number of type 1 cabinets:

1. Calculate the difference:

[tex]\( y - x = 80 - 30 \)[/tex]

[tex]\( = 50 \)[/tex]

So, 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 50.
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