A grocer mixes peanuts that cost $.49 per pound and chocolates that cost $.10 per pound to
make 100 pounds of a mixture that costs $18.19. How many pounds of peanuts is put into the
mixture?
Let's assume that the weight of peanuts added to the mixture is x pounds.
Since the total weight of the mixture is 100 pounds, the weight of the chocolates would be (100 - x) pounds.
The cost of peanuts per pound is $0.49, so the cost of x pounds of peanuts would be 0.49x dollars.
Similarly, the cost of chocolates per pound is $0.10, so the cost of (100 - x) pounds of chocolates would be 0.10(100 - x) dollars.
The total cost of the mixture is given as $18.19, so we can set up the equation:
0.49x + 0.10(100 - x) = 18.19
Simplifying the equation:
0.49x + 10 - 0.10x = 18.19
Combine like terms:
0.49x - 0.10x = 18.19 - 10
0.39x = 8.19
Divide both sides of the equation by 0.39 to solve for x:
x = 8.19 / 0.39
x ≈ 21
Therefore, approximately 21 pounds of peanuts would be put into the mixture.
To solve this problem, we can set up a system of equations based on the given information.
Let's assume that the number of pounds of peanuts is x.
The cost of peanuts is $0.49 per pound, so the cost of x pounds of peanuts is 0.49x dollars.
The cost of chocolates is $0.10 per pound, and since the grocer mixes 100 pounds of the mixture, the cost of chocolates is 0.10(100 - x) dollars.
The total cost of the mixture is given as $18.19.
So, we can set up the equation:
0.49x + 0.10(100 - x) = 18.19
Simplifying the equation:
0.49x + 10 - 0.10x = 18.19
0.49x - 0.10x = 18.19 - 10
0.39x = 8.19
Now, divide both sides of the equation by 0.39:
x = 8.19 / 0.39
x ≈ 21
Therefore, approximately 21 pounds of peanuts are put into the mixture.
just add up the value of each part, so the sum equals the whole
If there are x lbs of peanuts, then the rest (100-x) is chocolates. So,
.49x + .10(100-x) = 18.19