Answer:
- In the first week, the number of type-1 cabinets produced was 15,
- the number of type-2 cabinets produced was 30,
- the number of type-3 cabinets produced was 65.
Step-by-step explanation:
If we let a, b, c represent the numbers of type-1, type-2, and type-3 cabinets produced in the first week, respectively, we can write three equations in these unknowns:
- a + b + c = 110 . . . . . total cabinets for the first week
- a + 2b - c = 10 . . . . relationship of quantities in the first week
- 3a +0b +c = 110 . . . . total cabinets in the second week
It can be convenient to let a machine solver find the solution to this set of equations. Most graphing calculators can handle it, along with several web sites.
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Solving by hand, we can subtract the second equation from twice the first. This gives ...
2(a +b +c) -(a +2b -c) - 2(110) -(10)
a +3c = 210 . . . . simplify
Subtracting this from 3 times the third equation gives ...
3(3a +c) -(a +3c) = 3(110) -(210)
8a = 120 . . . . . simplify
a = 15 . . . . . . . divide by 8
Using this in the third equation of the original set, we have ...
3·15 +c = 110
c = 65 . . . . . . subtract 45
Then, in the first equation, we get ...
15 + b + 65 = 110
b = 30 . . . . . . . subtract 80
The solution is (type-1, type-2, type-3) = (15, 30, 65) for the first week.
