A botanist can purchase plant food of four different types, I, II, III, and IV. Each food comes in the same size bag, and the following table summarizes the number of grams of each of three nutrients that each bag contains. Food (grams) I II III IV Nutrient A 5 5 10 5 Nutrient B 10 5 30 10 Nutrient C 5 15 10 25 The botanist wants to use a food that has these nutrients in a different proportion and determines that he will need a total of 8,000 g of A, 18,000 g of B, and 14,000 g of C. Let
A botanist can purchase plant food of four different types, I, II, III, and IV. Each food comes in the same size bag, and the following table summarizes the number of grams of each of three nutrients that each bag contains. Food (grams) I II III IV Nutrient A 5 5 10 5 Nutrient B 10 5 30 10 Nutrient C 5 15 10 25 The botanist wants to use a food that has these nutrients in a different proportion and determines that he will need a total of 8,000 g of A, 18,000 g of B, and 14,000 g of C. Let
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.4: Applications
Problem 3EQ: A florist offers three sizes of flower arrangements containing roses, daisies, and chrysanthemums....
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A botanist can purchase plant food of four different types, I, II, III, and IV. Each food comes in the same size bag, and the following table summarizes the number of grams of each of three nutrients that each bag contains.
Food (grams) | ||||
---|---|---|---|---|
I | II | III | IV | |
Nutrient A | 5 | 5 | 10 | 5 |
Nutrient B | 10 | 5 | 30 | 10 |
Nutrient C | 5 | 15 | 10 | 25 |
The botanist wants to use a food that has these nutrients in a different proportion and determines that he will need a total of 8,000 g of A, 18,000 g of B, and 14,000 g of C. Let
x = Type I bags,
y = Type II bags,
z = Type III bags,
and
w = Type IV bags.
Write an equation for the total number of grams of Nutrient A in terms of x, y, z, and w.
Write an equation for the total number of grams of Nutrient B in terms of x, y, z, and w.
Write an equation for the total number of grams of Nutrient C in terms of x, y, z, and w.
Find the number of bags of each type of food that should be ordered. (If there are infinitely many solutions, express your answers in terms of w as in Example 3.)
(x, y, z, w) =
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