SOLUTION: Solve By Elimination:
Roast beef has 25 grams of protein and 11 grams of calcium per serving. A serving of mashed potatoes has 2 grams of protein and 25 grams of calcium. How many
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Roast beef has 25 grams of protein and 11 grams of calcium per serving. A serving of mashed potatoes has 2 grams of protein and 25 grams of calcium. How many
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Question 1123099: Solve By Elimination:
Roast beef has 25 grams of protein and 11 grams of calcium per serving. A serving of mashed potatoes has 2 grams of protein and 25 grams of calcium. How many servings of each are needed to supply exactly 29 grams of protein and 61 grams of calcium? Use b for servings of beef and m for servings of mashed potatoes. Answer by ikleyn(52788) (Show Source):
25*b + 2*m = 29 grams of protein (1)
11*b + 25*m = 61 grams of calcium (2)
Multiply eq(1) by 25 (both sides); multiply eq(2) by 2 (both sides). You will get
25*25*b + 50*m = 25*29 (3)
2*11*b + 50*m = 2*61 (4)
Subtract eq(4) fro eq(3). You will get
25*25*b - 2*11*b = 25*29-2*61, or
(25*25 - 2*11)*b = 25*29 - 2*61
b = = 1. (*) <<<---=== I specially / (intently) did not make intermediate calculations until I got this formula.
Then I copied the formula to Excel spreadsheet in my computer and calculated it "in one click".
Thus you just found "b" by elimination.
Now from eq(1), m = = 2.
Answer. b= 1, m= 2.
Solved.
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If you just know the determinant method (which is the same as the Cramer's rule),
you will easily recognize that the denominator in the formula (*) is the determinant of the coefficient matrix
to equations (1) and (2), while the numerator is the determinant of the modified matrix by the Cramer's rule.
When you use the Elimination method, it is an additional way to check that all your actions are / were correct.
