Question

Brand A bird seed is 20% sunflower seeds by weight. Brand B is 60% sunflower seed b weight. How many pounds of each must be mixed to get 50 pounds of bird seed that is 50% sunflower seed?

Answer 1

12.5 lb of Brand A and 37.5 lb of Brand B

Explanation:

Let a = weight of Brand A.

Let b = weight of Brand B.

To make 50 lb of bird seed, we get the equation:

a + b = 50

Now we deal with the amount of sunflower seed in each Brand and in the final mixture.

a amount of Brand A has 0.2a amount of sunflower seed.

b amount of Brand B has 0.6b amount of sunflower seed.

50 lb of the mixture has 0.5 × 50 lb = 25 lb of sunflower seed.

That gives us the second equation.

0.2a + 0.6b = 25

We have a system of equations:

a + b = 50

0.2a + 0.6b = 25

Solve the first equation for a and substitute in the second equation.

a = 50 - b

0.2(50 - b) + 0.6b = 25

10 - 0.2b + 0.6b = 25

0.4b + 10 = 25

0.4b = 15

b = 37.5

Now substitute 37.5 for b in the first original equation and solve for a.

a + 37.5 = 50

a = 12.5

12.5 lb of Brand A and 37.5 lb of Brand B