SOLUTION: Hello can someone please assist me with the correct approach to solving this problem? I would greatly appreciate it. Thanks in advance. Candy Mixtures - Someone wants to mix som

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Question 541055: Hello can someone please assist me with the correct approach to solving this problem? I would greatly appreciate it. Thanks in advance.
Candy Mixtures - Someone wants to mix some candy that is worth 45 cents per pound. Some is worth 80 cents per pound to make 350 lb of a mixture worth 65 cents per pound. How much of each type of candy should be used?

Found 2 solutions by oberobic, AnlytcPhil:
Answer by oberobic(2304) About Me  (Show Source):
You can put this solution on YOUR website!
You need to produce 350 lb of mixture.
x = amount of 45 cent candy
350-x = amount of 80 cent candy
.
45x + 80(350-x) = 65*350
.
45x + 28000 -80x = 22750
.
-35x = -5250
.
x = 150 lb of 45-cent candy
.
350-150 = 200 lb of 80-cent candy
.
This results in 350 lb of candy valued at 65 cents per lb.
.
To check the results...
150*45 = 6750
200*80 = 16000
6750+16000 = 22750
.
65*350 = 22750
.
Done.

Answer by AnlytcPhil(1806) About Me  (Show Source):
You can put this solution on YOUR website!
Candy Mixtures - Someone wants to mix some candy that is worth 45 cents per pound. Some is worth 80 cents per pound to make 350 lb of a mixture worth 65 cents per pound. How much of each type of candy should be used? 
Suppose we mix x pounds of the 45¢ candy with y pounds of the 80¢ candy.
Then we have two equations, a candy equation and a money equation:

The candy equation comes from this:

         %28matrix%286%2C1%2Cx%2C+pounds%2C+of%2C+less%2C+expensive%2C+candy%29%29 + %28matrix%286%2C1%2Cy%2C+pounds%2C+of%2C+more%2C+expensive%2Ccandy%29%29 = %28matrix%287%2C1%2C350%2C+pounds%2C+of%2C+medium%2C+priced%2C+mixed%2C+candy%29%29  


                          x + y = 350

The money equation comes from
    
          +  =   

                        (45¢)x + (80¢)y = (60¢)(350)  or
                              45x + 80y = 21000

So solve this system of equations:

                         x +   y =   350
                       45x + 80y = 21000

(If you can't solve that system of equations, post again asking how)

Answer: Mix 200 pounds of the less expensive candy and 150 pounds of the cheaper candy.

Edwin