Question

a farmer sells mixed nuts containing almonds at $4.00 per lb cashews at $2.50 per lb. how many pounds of each kind of nut will be in a 10-lb mixture that costs $2.95 per lb? show all work.

Answer 1

Let c=pounds of cashews, a=pounds of almonds then if we consider the weight,\[a+c=10\]and if we consider the money,\[2.5a+4c=2.95(10)\]These two equations are a system of linear equations that you can solve by substitution or elimination.

Answer 2

Can you get it from here?

Answer 3

so do i just plug in 10 to a and c?

Answer 4

Nope. Let's do a substitution.

Answer 5

The problem here is we have two variables, so we want to get rid of one. Which one do you want to keep?

Answer 6

i want to keep a.

Answer 7

So we rearrange the first equation to be\[c=10-a\]Do you see how I did that?

Answer 8

Yes.

Answer 9

Good. Now we substitute into the second equation. Replace c with 10-a. What do you get?

Answer 10

is the answer suppose to be a decimal?

Answer 11

I think it's something like \[2.5a+4(10-a)=29.5\]\[-1.5a=-10.5\]\[a=7\]\[\implies c=3\]So it looks like we need three pounds of cashews, and seven pounds of almonds.

Answer 12

Get it now?

Answer 13

Yes and thanks for the help.