- Judy, Scarlett, Phoebe, and Amanda all went through a weight loss diet program.
- Their combined weight loss after the program was equal to Scarlett's weight before the program.
- Judy's weight before the program was twice Phoebe's weight after the program.
- The combined weight of Scarlett, Phoebe and Amanda before the program was four times Phoebe's weight after the program.
- The combined weight of Judy and Scarlett before the program was thrice Scarlett's weight after the program.
- Phoebe and Amanda both lost the same amount of pounds.
- Twice Scarlett's weight loss was equal to thrice Amanda's weight loss.
- Scarlett lost 20 pounds more than Phoebe.
- The combined weight loss of Judy and Scarlett is equal to 140 pounds.
Determine the weights of Judy, Scarlett, Phoebe, and Amanda before and after the weight-loss program.
J and j were Judy's weight before and after, etc for the others.
Translating statements 2 through 9 into equations
S = (J+S+P+A) - (j+s+p+a)
J = 2p
S+P+A = 4p
J+S = 3s
P-p = A-a
2(S-s) = 3(A-a)
(S-s)= (P-p) + 20
(J-j) + (S-s) = 140
Spreadsheet Matrix using MINVERSE() and MMULT():
The leftmost column represents the statement number.
J S P A j s p a integer
2 1 0 1 1 -1 -1 -1 -1 0
3 1 0 0 0 0 0 -2 0 0
4 0 1 1 1 0 0 -4 0 0
5 1 1 0 0 0 -3 0 0 0
6 0 0 1 -1 0 0 -1 1 0
7 0 2 0 -3 0 -2 0 3 0
8 0 1 -1 0 0 -1 1 0 20
9 1 1 0 0 -1 -1 0 0 140
2 -2 0 0 1 1 -1 -1 2 260
3 -1 0 0 0 5 -2 4 1 220
4 -1 -0.5 0 0.5 3.5 -1.5 1.5 1 170
5 -2 -1.5 1 1.5 -6.5 1.5 -7.5 2 130
6 -2 0 0 1 4 -2 2 1 180
7 -1 0 0 0 2 -1 1 1 160
8 -1 -0.5 0 0.5 0.5 -0.5 -0.5 1 130
9 -2 -1.5 1 1.5 -8.5 2.5 -9.5 2 90
From 260, Judy lost 80 --------> 180
From 220, Scarlett lost 60 ----> 160
From 170, Phoebe lost 40 ---> 130
From 130, Amanda lost 40 ---> 90
Procedure for solving simultaneous equations using spreadsheet matrix functions.
I was using LibreOffice Calc, but I think it is the same for Excel.
The first 8x8 matrix is entered by hand: coefficients for the LHS of each equation.
The 1x8 column labelled "integer" is the RHS of each equation.
One then highlights an 8x8 area, enter "=MINVERSE(" select the first 8x8 matrix ")"
then hit Ctrl-Alt-Return rather than just Return
This produces the inverse of the first matrix.
Then highlight a 1x8 area; 8 rows, one column; a vertical array.
Type = "MMULT(" Select inverse matrix "," select the 1x8 column labelled 'integer' ")"
type Ctrl-Alt-Return
The solution magically appears; or an error.
Usually an error.
Edited on June 28, 2023, 8:09 pm
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Posted by Larry
on 2023-06-28 20:07:45 |
Spreadsheet matrix with instructions how to
