Question

Fertiliser is sold in 100kg bags labelled with the amount of nitrogen (N), phosphoric acid (P2O5), and potash (K2O) present. The mixture of these nutrients varies from one type of fertiliser to the next. 1 bag of Vigoro Ultra Turf fertiliser contains 29kg of nitrogen, 3kg of phosphoric acid, and 4kg of potash. 1 bag of Parkers Premium Starter fertiliser contains 18kg of nitrogen, 25kg of phosphoric acid, and 6kg of potash. How many bags of Vigoro Ultra Turf and Parkers Premium Starter would you require in order to make a fertiliser mixture containing 217kg of nitrogen, 115kg of phosphoric acid, and 44kg of potash

Answer 1

We need 5 bags of Vigoro Ultra Turf and 4 bags of Parkers Premium fertilizer.

Explanation:

Let's first list the percentage compositions of each fertilizer type:

Vigoro Ultra Turf:

Nitrogen (N) = 29 kg

Phosphoric Acid (P2O5) = 3 kg

Potash (K2O) = 4 kg

Parkers Premium

Nitrogen (N) = 18 kg

Phosphoric Acid (P2O5) = 25 kg

Potash (K2O) = 6 kg

We can set up simultaneous equations to find out the amount of 100 kg bags of each fertilizer needed:

x = Vigoro Ultra turf (one bag)

y = Parkers Premium (one bag)

29x + 18y = 217 -Equation 1

3x + 25y = 115 -Equation 2

4x + 6y = 44 -Equation 3

Solving for x and y, we get:

x = 5

y = 4

This means we need 5 bags of Vigoro Ultra Turf and 4 bags of Parkers Premium fertilizer.