How many pounds of each did she use?

Question

The owner of a candy store wants to mix some peanuts worth $2 per pound, some cashews worth $10 per pound, and some Brazil nuts worth $9 per pound to get 50 pounds of a mixture that will sell for $6.40 per pound. She uses 10 fewer pounds of cashews than peanuts. How many pounds of each did she use?

Answer 1

Lets make our variables p, c, and b for peanuts, cashews, and Brazil nuts respectively.

Here's what we know:

p + c + b = 50

2p + 10c + 9b = 50*6.40 --> 320

c = p - 10

 

Let's put our variable in and see what we're left with when we finish simplifying:

p + (p - 10) + b = 50

2p + 10(p - 10) + 9b = 320

 

2p - 10 + b = 50

12p - 100 + 9b = 320

 

2p + b = 60

12p + 9b = 420

 

We can see a single b in that first equation, so if we isolate that, we can easily substitute that into the other equation:

b = 60 - 2p

 

12p + 9(60 - 2p) = 420

12p + 540 - 18p = 420

-6p + 540 = 420

-6p = -120

p = 20

 

Now that we have p, we can find out c and b:

c = 20 - 10

c = 10

b = 60 - 2*20

b = 60 - 40

b = 20

 

Now that we have our numerical values, we can check our answer:

20 + 10 + 20 = 50

2*20 + 10*10 + 9*20 = 320

40 + 100 + 180 = 320

100 + 220 = 320

320 = 320

 

So we have 20 lbs of peanuts, 10 lbs of cashews, and 20 lbs of Brazil nuts.