The owner of a pet food store wants to mix birdseed that costs $1.25 per pound with sunflower seed that cost $0.75 per pound to make 50 pounds of a mixture that costs $1.00 per pound. How many pounds of each type of seed should he use?

Question
Equations and inequalities
asked 2020-12-16
The owner of a pet food store wants to mix birdseed that costs $1.25 per pound with sunflower seed that cost $0.75 per pound to make 50 pounds of a mixture that costs $1.00 per pound. How many pounds of each type of seed should he use?

Answers (1)

2020-12-17
Let x be the amount of birdseed and yy be the amount of sunflower seeds, both in pounds.
The mixture must be 50 pounds:
\(\displaystyle{x}+{y}={50}{\left({1}\right)}\)
In terms of cost,
\(\displaystyle{1.25}{x}+{0.75}{y}={1}{\left({50}\right)}\)
or
\(\displaystyle{1.25}{x}+{0.75}{y}={50}{\left({2}\right)}\)
Solve for yy using (1) to obtain (3):
\(\displaystyle{y}={50}−{x}{\left({3}\right)}\)
Substitute (3) to (2) and solve for x:
\(\displaystyle{1.25}{x}+{0.75}{\left({50}−{x}\right)}={50}\)
\(\displaystyle{1.25}{x}+{37.5}−{0.75}{x}={50}\)
\(\displaystyle{0.5}{x}={12.5}\)
\(\displaystyle{x}={25}\)
Solve for yy using (3):
\(\displaystyle{y}={50}−{25}\)
\(\displaystyle{y}={25}\)
So, the owner should use 25 pounds of birdseed and 25 pounds of sunflower seeds.
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