Mathematics - Linear Simultaneous Equations
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A ceramics workshop makes wreaths, trees, and sleighs for sale at Christmas. A wreath takes 3 hours to prepare, 2 hours to paint, and 8 hours to fire. A tree takes 16 hours to prepare, 3 hours to paint, and 4 hours to fire. A sleigh takes 4 hours to prepare, 17 hours to paint, and 7 hours to fire. If the workshop has 113 hours for prep time, 80 hours for painting, and 97 hours for firing, how may of each can be made?
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Solution Summary
Linear simultaneous equations are determined. A neat and step-by-step solution is attached.
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A ceramics workshop makes wreaths, trees, and sleighs for sale at Christmas. A wreath takes 3 hours to prepare, 2 hours to paint, and 8 hours to fire. A tree takes 16 hours to prepare, 3 hours to paint, and 4 hours to fire. A sleigh takes 4 hours to prepare, 17 hours to paint, and 7 hours to fire. If the workshop has 113 hours for prep time, 80 hours for painting, and 97 hours for firing, how may of each can be made?
Let x wreaths, y trees and z sleighs be made. Then from the data of the problem, we can make the set of equations...
3x+ 16y + 4z = 113 (Preparation time)
2x + 3y + 17z = 80 (Painting time)
8x + 4y + 7z = 97 (Firing time)
We solve this system of equations as shown below.
Row
Operation
1: 3 16 4 113
2 3 17 80
8 4 7 97
multiply the 1st row by 1/3 1 16
________________________________________ 3 4
________________________________________ 3 113
________________________________________ 3
2 3 17 80
8 4 7 97
Row
Operation
2: 1 16
________________________________________ 3 4
________________________________________ 3 113
________________________________________ 3
2 3 17 80
8 4 7 97
add -2 times the 1st row to the 2nd row 1 16
________________________________________ 3 4
________________________________________ 3 113
________________________________________ 3
0 -23
________________________________________ 3 43
________________________________________ 3 14
________________________________________ 3
8 4 7 97
Row
Operation
3: ...
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