SOLUTION: The Cashew Company is making a mixture worth $76.88 using 7 pounds of cashews, 2 pounds of almonds and 5 pounds of peanuts. The cashews cost three times as much as the peanu

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Question 1015996: The Cashew Company is making a mixture worth $76.88
using 7 pounds of cashews, 2 pounds of almonds and
5 pounds of peanuts. The cashews cost three times
as much as the peanuts and the almonds cost 18
times as much as the peanuts. What is the price of
a pound of the cashews?
Found 2 solutions by macston, Edwin McCravy:
Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
.
I do not think you proof read your problem,
but this will show you how to find the answer
with the correct numbers.
.
P=cost of peanuts; C=cost of cashews=3P; A=cost of almonds=218218P
Total weight of mix= 7 pounds + 2 pounds + 5 pounds = 14 pounds
.
(7lbs)C+(2lbs)A+(5lbs)P=(14lbs)$76.88
(7lbs)(3P)+(2lbs)(218218P)+(5lbs)(P)=1076.32
21P+436436P+5P=1076.32
436462P=1076.32
P=$0.0025 per pound
Peanuts cost 0.25 cents per pond
.
C=3P=3($0.0025/pound)=$0.0075/pound
.
ANSWER: Cashews cost $0.0075 per pound (3/4 cent per pound)
.
CHECK:
.
A=218218P=218218($0.0025)=$538.13 per pound
Almonds cost $5338.13 per pound
.
(7lbs)C+(2lbs)A+(5lbs)P=(14lbs)$76.88
(7lbs)($0.0075/lb)+(2lbs)($538.13/lb)+(5lbs)($0.0025/lb)=(14lbs)$76.88
$0.0525+$1076.26+$0.0125=$1076.32
$1076.325=$1076.32 (.005 cent discrepancy from rounding)








Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
I didn't believe you meant to type "218218".  I saw
18 in there twice and assumed you meant to type 18,
and changed it to 18.

The Cashew Company is making a mixture worth $76.88 
using 7 pounds of cashews, 2 pounds of almonds and 
5 pounds of peanuts.  The cashews cost three times 
as much as the peanuts and the almonds cost 18 
times as much as the peanuts. What is the price of
a pound of the cashews?

Let c = the price of a pound of cashews.
Let a = the price of a pound of almonds.
Let p = the price of a pound of peanuts.

7c + 2a + 5p = 76.88
           c = 3p
           a = 18p

7(3p) +2(18p) +5p = 76.88
   21p + 36p + 5p = 76.88
              62p = 76.88
                p = 1.24

The price of a pound of peanuts is $1.24.
The price of a pound of almonds is 18($1.24) or $22.32.
The price of a pound of cashews is 3($1.24) or $3.72.


Edwin