SOLUTION: How many pounds of candy worth $0.50 per pound and how many pounds of peanuts worth $0.90 per pound must be mixed to get a mixture of 64 pounds worth $0.60 per pound? I need to wri

Question 45317This question is from textbook Intermediate Algebra
: How many pounds of candy worth $0.50 per pound and how many pounds of peanuts worth $0.90 per pound must be mixed to get a mixture of 64 pounds worth $0.60 per pound? I need to write the equation and solve it.
Gracias.
Lydia Alejandro. This question is from textbook Intermediate Algebra

Answer by tutmath(14) (Show Source): You can put this solution on YOUR website!
Let the pounds of candy to be mixed be x pounds and the pounds of peanut to be mixed be y pounds.
Now the total pounds of the mixture is 64 as stated in the problem.
Hence the first equation we have is x + y = 64,
can also be written as x = 64 - y
Now candy is worth $0.50 / pound, if there are x pounds of candy then they will be worth 0.50 times x = 0.5x dollars
Similarly, peanut is worth $0.90 / pound, hence y pounds of peanut will be worth 0.9y dollars.
The problem states the total mixture is worth $0.6 / pound and weighs 64 lbs.
Hence the total mixture amounts to 0.6 * 64 = $38.4
Since the mixture is x pounds of candy and y pounds of peanut, we can equate the total dollar values as:
0.5x + 0.9y = 0.6 (64) = 38.4 (this is the second equation)
But we know x = 64 - y (from the first equation)
Therefore substituting this value of x in the second equation,
0.5(64 - y) + 0.9y = 38.4
32 - 0.5y + 0.9y = 38.4
0.4y = 6.4
y = 16
x = 64 - y = 64 - 16 = 48
(If you have any questions on the solution you can send me your queries at tutmath@gmail.com)
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