SOLUTION: Hi is there a way of working out how many 3 course meals and 2 course meals (single courses must be calculated as a three course) from the value of starters, mains and desserts giv

Question 891813: Hi is there a way of working out how many 3 course meals and 2 course meals (single courses must be calculated as a three course) from the value of starters, mains and desserts given to a table?
For example, a table has 10 starters, 12 mains and 8 desserts, is there an equation that can be used to calculate how many 2 course and 3 course options were given at the table?
I hope this makes sense and that it is possible.
Thanks
Simon
Answer by richwmiller(17219) (Show Source): You can put this solution on YOUR website!
What is included in a two course meal?
starts and main?
main and dessert?
Under these circumstances we have three unknowns and three equations
w= three course
x= starters and main
y= main and dessert
w+x+0*y=10
w+0*x+y=8
w+x+y=12
1,1,0,10
1,0,1,8
1,1,1,12
add down (-1/1) *row 1 to row 2
1,1,0,10
0,-1,1,-2
1,1,1,12
add down (-1/1) *row 1 to row 3
1,1,0,10
0,-1,1,-2
0,0,1,2
divide row 2 by -1/1
1,1,0,10
0,1,-1,2
0,0,1,2
add down (0/1) *row 2 to row 3
1,1,0,10
0,1,-1,2
0,0,1,2

We now have the value for the last variable.
We will work our way up and get the other solutions.
add up (1/1) *row 3 to row 2
1,1,0,10
0,1,0,4
0,0,1,2
add up (0/1) *row 3 to row 1
1,1,0,10
0,1,0,4
0,0,1,2
add up (-1/1) *row 2 to row 1
1,0,0,6
0,1,0,4
0,0,1,2
final
1,0,0,6
0,1,0,4
0,0,1,2
6 three course
4 starters and main
2 main and dessert
10 starters
12 main
8 dessert
"6","4","2"
(6,4,2)

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