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?

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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?

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Answer 1 · 2015-06-04T21:29:15

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 · 2015-06-04T21:38:35

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.

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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?

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