Question

A 5-lb nut mixture is worth $2.80 per pound. The mixture contains peanuts worth $1.70 per pound and cashews worth $4.55 per pound. How many pounds of each type of nut are int he mixture?

Answer 1

Let's call the amount of cashew nuts `x`

Then the amount of peanuts is `5-x` because we have 5 lbs in total.
5 lbs of mixture is `2.80*5=$14.00`

This is equal to `$1.70*(5-x)+$4.55*x=$14.00`

Now work away the brackets first, keep all the `x`'s on the left, and put the dollars to the right, divide, and you'll find `x`, the amount of cashew nuts. The rest is peanuts :-)

Answer 2

Let `x in [0, 1]` be the weight of cashews in one pound of mixture.

Then one pound of mixture contains `(1-x)` pounds of peanuts.

Equating the costs in dollars, we have:

`2.80 = 1.70(1-x) + 4.55x`

`=1.70-1.70x+4.55x`

`=1.70+2.85x`

Subtract `1.70` from both ends to get:

`2.85x = 1.10`

So `x = 1.10/2.85 = 110/285 = 22/57` pounds of cashews per pound of mixture

and `1-x = 1-22/57 = 35/57` pounds of peanuts per pound of mixture

In 5-lb of mixture there is `5*22/57 ~= 1.93` lb of cashews
and `5*35/57 ~= 3.07` lb of peanuts.