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The granular fertilizer 11​-11​-11 is composed of 11​% ​nitrogen, 11​% ​phosphate, and 11​% potassium.​ similarly, the fertilizer 19​-17​-0 is composed of 19​% ​nitrogen, 17​% ​phosphate, and 0​% potassium. If a gardener mixes a 5 pound bag of 11​-11​-11 with a 25 pound bag of 19​-17​-0​, what are the concentrations of​ nitrogen, phosphate, and potassium in the​ mixture? Express the answers as percents.

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znk

The farmer would get 30 lb of 18-16-2 fertilizer.

We can use a variation of the dilution formula to solve this problem.

V₁c₁ + V₂c₂ = V₃c₃

For N

5 lb × 11 + 25 lb × 19 = 30 lb × x

55 + 475 = 30x

x = 530/30 = 18

For PO₄

5 lb × 11 + 25 lb × 17 = 30 lb × y

55 + 425 = 30y

y = 480/30 = 16

For K

5 lb × 11 + 25 lb × 0 = 30 lb × z

55 + 0 = 30z

x = 55/30 = 2

The farmer would get 30 lb of 18-16-2 fertilizer.

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