SOLUTION: A store buys granola at $1/lb and dried fruit at $2/lb. and sells them at 25% markup. The store sells 2 special mixtures of granola and dried fruit. One customer buys 6 lbs. of Mi
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Question 366975: A store buys granola at $1/lb and dried fruit at $2/lb. and sells them at 25% markup. The store sells 2 special mixtures of granola and dried fruit. One customer buys 6 lbs. of Mixture A and 4 lbs of Mixture B and pays $17. Another custoemr reverses the proportions and pays a dollar more.
What is the recipe for Mixture A?
What is the recipe for Mixture B? Found 2 solutions by mananth, amoresroy:Answer by mananth(16946) (Show Source):
You can put this solution on YOUR website! 6 lbs. of Mixture A number of pounds be x
4 lbs of Mixture B number of pounds be y
and pays $17.
6x+4y=17.....................................1
Another customer reverses the proportions
and pays a dollar more.
6y+4x=18.....................................2
...
multiply 1 by -4 & 2 by 6
-24x-16y=-68
36y+24x=108
..
add up
20y=40
/20
y = 2 price of Mixture B
plug value of y in
6x+4y=17
6x+8=17
6x=9
/6
x= 3/2 the price of mixture A
...
m.ananth@hotmail.ca
You can put this solution on YOUR website! A store buys granola at $1/lb and dried fruit at $2/lb. and sells them at 25% markup. The store sells 2 special mixtures of granola and dried fruit. One customer buys 6 lbs. of Mixture A and 4 lbs of Mixture B and pays $17. Another custoemr reverses the proportions and pays a dollar more.
Given:
Selling Prices
Granola : $1 plus 25% mark-up = $1.25/lb
Dried Fruit : $2 plus 25% mark-up = $2.50/lb
Let A = Selling price of mixture A
B = Selling price of mixture B
Equation 1
6A + 4B = 17
Equation 2
4A + 6B = 18
multiply equation 2 by 1.5
6A + 9B = 27
deduct equation 2 by equation 1
(6A-6A)+ (9B-4B) = 27 -17
5B = 10
B = 2
substitute B=2 in equation1
6A + 4(2) = 17
6A = 17-8
A = 1.5
If mixtures A & B is sold at Granola = $1 plus 25% mark-up = $1.25/lb
& $2.00/lb respectively, we ca now compute the recipe for mixtures A & B
Given
Selling prices
Mixture A = $1.50/lb
Mixture B = $2.00/lb
Let x = % of Granola in mixture A
1.25x + 2.5(1-x) = 1.5
x = 80%
So recipe for mixture A is 80% Granola & 20% Dried Fruit
Let y = % 0f Granola in mixture B
1.25 y + 2.5(1-y) = 2
y = 40%
So recipe for mixture B is 40% Granola & 60% Dried Fruit
