Answered

At Westonci.ca, we make it easy to get the answers you need from a community of informed and experienced contributors. Get immediate and reliable solutions to your questions from a community of experienced professionals on our platform. Get precise and detailed answers to your questions from a knowledgeable community of experts on our Q&A platform.

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.
We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. We're here to help at Westonci.ca. Keep visiting for the best answers to your questions.