Question

# The owner of a pet food store wants to mix birdseed that costs $1.25 per pound with sunflower seeds that cost$0.75 pe pound to make 50 pounds of a mi

Equations and inequalities
The owner of a pet food store wants to mix birdseed that costs $1.25 per pound with sunflower seeds that cost$0.75 pe 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?

2021-05-04
2021-08-04

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.