Answer:
12.5 lb of Brand A and 37.5 lb of Brand B
Step-by-step 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
