SOLUTION: A mixture of nuts contains almonds worth .50 cents a pound, cashews worth $1.00 per pound, and pecans worth .75 cents per pound. If there are three times as many pounds of almonds
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Question 210703This question is from textbook College Algebra
: A mixture of nuts contains almonds worth .50 cents a pound, cashews worth $1.00 per pound, and pecans worth .75 cents per pound. If there are three times as many pounds of almonds as cashews in a 100-pound mixture worth .70 cents per pound, how many pounds of each nut does the mixture contain?
This question is from textbook College Algebra
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
mixture of nuts contains almonds worth .50 cents a pound, cashews worth $1.00
per pound, and pecans worth .75 cents per pound.
If there are three times as many pounds of almonds as cashews in a 100-pound
mixture worth .70 cents per pound, how many pounds of each nut does the mixture contain?
:
Let a = no. of lbs of almonds
Let c = no. of lbs of cashews
Let p = no. of lbs of pecans
:
.50a + 1.00c + .75p = .70(100)
:
"three times as many pounds of almonds as cashews"
a = 3c
then we can say
p = (100 - a - c)
Replace a with 3c
p = (100 - 3c - c)
p = (100-4c)
:
.5a + 1.00c + .75p = .70(100)
Replace a and p with the above expressions
.5(3c) + 1(c) + .75(100-4c) = .70(100)
:
1.5c + c + 75 - 3c = 70
:
1.5c + c - 3c = 70 - 75
:
-.5c = -5
c =
c = +10 lb of cashews
then
3*10 = 30 lb almonds
and
10 - 40 = 60 lb of pecans
:
:
Check solution in original equation
.50(30) + 1.00(10) + .75(60) = .70(100)
15 + 10 + 45 = 70
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