SOLUTION: I am stuck on this linear equation story problem. I was hoping someone could please help me with the formula that I need. The Candy Shop wants to create 50 pounds of a holiday m

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Question 143396This question is from textbook Mathematical Ideas
: I am stuck on this linear equation story problem. I was hoping someone could please help me with the formula that I need.
The Candy Shop wants to create 50 pounds of a holiday mix that will sell for $3.91 per pound. How many pounds of a candy selling for $2.59 per pound should be combined with candy selling for $6.99 per pound to create the desired mix?
Set up a system of equations to describe this situation. Solve the system of equations to find the solution.
This isn't from a book, it is from a problem in one of my online classes. Thanks so much ~Lyn This question is from textbook Mathematical Ideas

Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website!
he Candy Shop wants to create 50 pounds of a holiday mix that will sell for $3.91 per pound. How many pounds of a candy selling for $2.59 per pound should be combined with candy selling for $6.99 per pound to create the desired mix?
Set up a system of equations to describe this situation. Solve the system of equations to find the solution.
:
Let x = amt of 2.59 candy required (to make a 50 lb mixture)
Let y = amt of 6.99 candy required
:
Total lb amt equation:
x + y = 50
y = (50-x); use this for substitution
:
The $ value equation:
2.59x + 6.99y = 3.91(50)
:
2.59x + 6.99y = 195.50
:
Substitute (50-x) for y in the above equation, find x:
2.59x + 6.99(50-x) = 195.50
:
2.59x + 349.50 - 6.99x = 195.50
:
2.59x - 6.99x = 195.50 - 349.50
;
-4.40x = -154
x =
x = +35 lb of $2.59 candy
:
Then y = 50 - 35 = 15 lb of $6.99 candy
;
:
Check solutions in the $$ equation:
2.59(35) + 6.99(15) = 195.50
90.65 + 104.85 = 195.50