Question

A birdseed manufacturer wants to mix millet worth 28 cents a kilogram and grain worth 18 cents a kilogram to make 500 kilograms of birdseed worth 24 cents a kilogram. solve the equation ton find out how many kilograms of each seed should be used

Answer 1

Let x be the number of kilograms of millet and y be the number of kilograms of grain.

We want to solve the system of equations:

x + y = 500 (total weight of birdseed)

0.28x + 0.18y = 0.24(500) (total cost of birdseed)

Simplifying the second equation:

0.28x + 0.18y = 120

Multiplying the first equation by 0.28 and subtracting it from the second equation, we get:

0.28x + 0.18y - 0.28x - 0.28y = 120 - 0.28(500)

-0.10y = -40

y = 400

Substituting y = 400 into the first equation, we get:

x + 400 = 500

x = 100

Therefore, the manufacturer should use 100 kg of millet and 400 kg of grain to make 500 kg of birdseed worth 24 cents a kilogram.