Pistachios cost $6.50/pound and Almonds cost $8.00/pound. How much of each to make a 50lb mixture that costs $7.50/pound?

Any help in the right direction would be great!

Question

Pistachios cost $6.50/pound and Almonds cost $8.00/pound. How much of each to make a 50lb mixture that costs $7.50/pound?

Any help in the right direction would be great!

anonymous · Answer

This took a few to figure out. Bear with me while I show the work.

anonymous · Answer

Aright.

anonymous · Answer

Main problem setup:
$$6.5x+8y=7.50(50)=375$$
We know that x+y=50.
Solving for y we get y=50-x.
Substituting back into the original problem:
$$6.5x+8(50-x)=375$$
$$6.5x+400-8x=375$$
$$-1.5x=-25$$
$$x=16+2/3$$
From the earlier equation we can calculate y:
$$y=50-(16+2/3)=33+1/3$$

anonymous · Answer

If you plug the values back into the the original problem you get $375