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
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
