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.

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.