SOLUTION: A gift store is making a mixture of almonds, pecans, and peanuts, which sells for $4.50 per pound, $4 per pound, and $3 per pound, respectively. The storekeeper wants to make 50 po

Question 869897: A gift store is making a mixture of almonds, pecans, and peanuts, which sells for $4.50 per pound, $4 per pound, and $3 per pound, respectively. The storekeeper wants to make 50 pounds of mix to sell at $4.30 per pound. The number of pounds of peanuts is to be three times the number of pounds of pecans. Find the number of pounds of each to be used in the mixture.
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A gift store is making a mixture of almonds, pecans, and peanuts, which sells for $4.50 per pound, $4 per pound, and $3 per pound, respectively.
The storekeeper wants to make 50 pounds of mix to sell at $4.30 per pound.
The number of pounds of peanuts is to be three times the number of pounds of pecans.
Find the number of pounds of each to be used in the mixture.
:
let a = no. of lbs of almonds required
let p = amt of pecans
let n = amt of peanuts
:
The total amt equation
a + p + n = 50
:
the cost mixture equation
4.50a + 4p + 3n = 4.30(50)
4.50a + 4p + 3n = 215
:
"The number of pounds of peanuts is to be three times the number of pounds of pecans."
n = 3p
:
Replace n with 3p in the 1st two equations
a + p + 3p = 50
a + 4p = 50
a = (50-4p); we can use this form for substitution
and
4.5a + 4p + 3(3p) = 215
4.5a + 4p + 9p = 215
4.5a + 13p = 215
replace a with (50-4p)
4.5(50-4p) + 13p = 215
225 - 18p + 13p = 215
-18p + 13p = 215 - 225
-5p = -10
p = -10/-5
p = 2 lb of pecans
then
a = 50 - 4p
a = 50 - 4(2)
a = 42 lb of almonds
and
42 + 2 + n = 50
n = 50 - 44
n = 6 lb of nuts
:
;
:
Check this in the cost/mixture equation
4.50a + 4p + 3n = 215
4.5(42) + 4(2) + 3(6) = 215
189 + 8 + 18 = 215
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