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Sagot :
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.
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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