Question

Birdseed costs $0.52 a pound and sunflower seeds cost $0.82 a pound. Angela wishes to make a 40 pound mixture of birdseed and sunflower seeds that sells for 0.66 per pound. How many pounds of each type of seed should she use?

Answer 1

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:

`\begin{gathered} b+s=40 \\ 0.52b+0.82s=40\cdot0.66 \end{gathered}`

Solving the first equation for b, and substituting in the second equation we get:

`\begin{gathered} 0.52(40-s)+0.82s=26.4 \\ 20.8-0.52s+0.82s=26.4 \\ 0.30s=5.6 \\ s=18(2)/(3) \end{gathered}`

Substituting s=18 2/3 in the first equation, and solving for b we get:

`\begin{gathered} b+18(2)/(3)=40 \\ b=21(1)/(3) \end{gathered}`

Therefore she should use 21 1/3 pounds of birdseed and 18 2/3 pounds of sunflower seed.