Let b be the number of pounds of birdseed in the mixture, and s be the number of pounds of sunflower seeds, then we can set the following system of equations:
[tex]\begin{gathered} b+s=40 \\ 0.52b+0.82s=40\cdot0.66 \end{gathered}[/tex]Solving the first equation for b, and substituting in the second equation we get:
[tex]\begin{gathered} 0.52(40-s)+0.82s=26.4 \\ 20.8-0.52s+0.82s=26.4 \\ 0.30s=5.6 \\ s=18\frac{2}{3} \end{gathered}[/tex]Substituting s=18 2/3 in the first equation, and solving for b we get:
[tex]\begin{gathered} b+18\frac{2}{3}=40 \\ b=21\frac{1}{3} \end{gathered}[/tex]Therefore she should use 21 1/3 pounds of birdseed and 18 2/3 pounds of sunflower seed.
