SOLUTION: There�re three brand of fertilizers A, B, and C. Following is a table of the amount of nitrogen, phosphorus, and potassium in a box of each brand (in lb). Brand A B C N 1 2

Question 607291: There�re three brand of fertilizers A, B, and C. Following is a table of the amount of nitrogen, phosphorus,
and potassium in a box of each brand (in lb).
Brand A B C
N 1 2 2
P 2 1 2
K 2 2 1

How many boxes of each brand are needed in order to make a mixture that contains 6 lb of nitrogen, 6 lb of phosphorus and 7 lb of potassium?

Answer by LisaJ(11) (Show Source): You can put this solution on YOUR website!
Set your variables:
a = boxes of A
b = boxes of B
c = boxes of C
You will get three equations:
1: For N: a + 2b + 2c = 6
2: For P: 2a + b + 2c = 6
3: For K: 2a + 2b + c = 7
Solve using determinants, if you have studied them. Otherwise solve by elimination of variables:
Subtract the second equation from the first:
-a + b = 0
So a=b.
..
Substitute b = a into Eq. 1: 3a + 2c = 6
Substitute b = a into Eq. 3: 4a + c = 7
Solve these together for a = 8/3; c = 3/5.

RELATED QUESTIONS
One type of lawn fertilizer consists of a mixture of Nitrogen, N, Phosphorus, P, and... (answered by rwm)

A farmer uses two types of fertilizers. A 50-lb bag of Fertilizer A contains 8 lb of... (answered by Theo)

A farmer uses two types of fertilizers. A 50-lb bag of Fertilizer A contains 8 lb of... (answered by ikleyn)

by weight one fertilizer is 20% potassium, 30% nitrogen and 50% phosphorus. a second... (answered by Theo)

The ratio of nitrogen to phosphorus to potash in a fertilizer is 7 : 5 : 3. If there are... (answered by rapaljer)

Soil contains a wide variety of nutrients, including nitrogen, phosphorus, potassium,... (answered by ikleyn)

Brand A fertilizer is 32% phosphorus and Brand B is 18% phosphorus. How much of each... (answered by richwmiller)

A horticulturist wants to mix three types of fertilizers, which contain 20%, 30%, 40%... (answered by Jk22)

a soil analysis of a lawn determines that 50 pounds of fertilizeer containing 20 %... (answered by josmiceli)