Alg 2 word problem help plz?

Question

You plan to create a mixture of nuts for the holiday season. You want to mix cashews and walnuts to sell for $2 per pound. Walnuts cost $1.50 per pound and cashews cost $3 per pound. If you want to have a total of 60 pounds of your mixture, then how many pounds of cashews and how many pounds of walnuts must you buy to sell your mixture at $2 per pound?

I read it a few times and it looks like it might be easy, but im stumped. if its not too much can someone please help me? thank you very much :)

Answer 1

tell ur teacher to stop give u some stupid question.!!

Answer 2

w = # lbs of Walnuts

c = # lbs of Cashews

(1) w + c =60

(2) w*1.5 + c*3 = 120 (because is 60lbs  @ $2 per lb)

(3) c=60-w From (1)

Replace (3) in (2)

w*1.5 + (60 - w)*3 = 120

w*1.5 + 180 - w*3 = 120

180 - 120 = w*3 - w*1.5

60 = w*1.5

60/1.5=w

40=w

Replace w in (3)

c=60-40

answer:

w= 40 lbs of Walnuts

c= 20 lbs of Cashews

Answer 3

Here's how I solved it.  If I put one pound of walnuts with one pound of cashews I will have two pounds of a mix that costs $4.50, or $2.25 per pound.  Since I want a mixture that costs $2.00 per pound I know that I need to use a smaller amount of cashews (that cost more) and more of the walnuts that cost less.  So then I thought, how about making a two pound mixture that has $2 worth of walnuts and $2 worth of cashews.  Then I figured that $2 worth of walnuts would be $1.50 for the first pound, so how many pounds of walnuts do I get for $.50?  I know that $.50 is one third of $1.50, so for $2, I can buy one and one third pounds of walnuts.  Next, how many pounds of cashews can I buy for $2?   They cost $3 a pound so I can buy 2/3 of a pound.   Aha!   I can make a two pound mixture of walnuts and cashews for $4 by buying one and one-third pounds of walnuts and two-thirds of a pound of cashews.  Each one pound of my mix contains one half of one and one third pounds of walnuts (1/2 of 1 1/3 is 1/2 of 4/3 which is 2/3) and one half of two-thirds pound of cashews (1/2 of 2/3 is 1/3).   So to make 60 pounds of my mixture I need 60 times 2/3 pounds of walnuts and 60 times 1/3 pounds of cashews.  I bet you can finish that calculation.   When you are stumped, be sure to start trying to show the problem by drawing pictures, or charts, etc.  It can help you think things through.  That's how I do it.

(They seem to have left out any consideration of profit margin in this problem. It must not be a money-making operation.)

Answer 4

w = # of walnuts, c = # of cashews

1) w + c = 60

w = 60 - c

2) 1.5w + 3c = 2(60)

1.5(60 - c) + 3c = 120

90 - 1.5c + 3c = 120

1.5c = 30

c = 20

w = 60 - 20 = 40

NOTE!!! This result gives you a mixture of 60 # that COSTS $2/#

Hopefully, you will sell at more that $2/#