Question 1086441: The Divine Chocolate store want to create a new truffle mix that consists of milk chocolate and hazelnut. If hazelnuts sell for $6 per pound and milk chocolate sells for $3 per pound, how many pounds of each should they mix together to create a six-pound box that sells for $5 per pound?
How would I go about setting this up? If you could show me how to set the problem up I could answer it. Thank you!
Found 2 solutions by jorel1380, ikleyn:
Answer by jorel1380(3719)   (Show Source):
Answer by ikleyn(52785)  (Show Source):
You can put this solution on YOUR website! .
The Divine Chocolate store want to create a new truffle mix that consists of milk chocolate and hazelnut.
If hazelnuts sell for $6 per pound and milk chocolate sells for $3 per pound, how many pounds of each should they mix together
to create a six-pound box that sells for $5 per pound?
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Take x (now unknown) pounds of milk chocolate and y (now unknown) pounds of hazelnuts.
Then the total mass of the mix is x+y pounds, and your equations are
x + y = 6 (1) (total mass equation in pounds)
6x + 3y = 5*6 (2) (total value in dollars)
In other words,
x + y = 6, (1)
6x + 3y = 30. (2)
From equation (1) express x = 6 - y and substitute it into the equation (2).
You will get a single equation for single unknown y:
6*(6-y) + 3y = 30.
Simplify and solve for y:
36 - 6y + 3y = 30, or
-3y = 30 - 36,
-3y = -6,
y =  = 2.
Thus you found the unknown y. It is 2.
So you need to use 2 pounds of hazelnuts.
Then the mass of milk chocolate is 6 - 2 = 4 pounds.
Answer. Mix 4 pounds of milk chocolate with 2 pounds of hazelnuts.
Solved.
There is entire bunch of lessons covering various types of mixture problems
- Mixture problems
- More Mixture problems
- Solving typical word problems on mixtures for solutions
- Word problems on mixtures for antifreeze solutions
- Word problems on mixtures for dry substances like coffee beans, nuts, cashew and peanuts
- Word problems on mixtures for dry substances like candies, dried fruits
- Word problems on mixtures for dry substances like soil and sand
- Word problems on mixtures for alloys
- Typical word problems on mixtures from the archive
- OVERVIEW of lessons on word problems for mixtures
in this site.
Read them and become an expert in solution the mixture word problems.
Also, you have this free of charge online textbook in ALGEBRA-I in this site
- ALGEBRA-I - YOUR ONLINE TEXTBOOK.
The referred lessons are the part of this online textbook under the topic "Mixture problems
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