Ellen wishes to mix candy worth $1.64 per pound with candy worth $3.46 per pound to form 20 pounds of mixture worth $3.00 per pound. How many pounds of the more expensive candy should she use?
let the amount of expensive candy be x pounds
then the amound of cheaper candy would be 2-x pounds
solve for x:
3.46x + 1.64(20-x) = 3.00(20)
I suggest multiplying each of the three terms by 100
Thank you Reiny!
Let's assume Ellen uses x pounds of the candy worth $3.46 per pound.
The total weight of the candy worth $1.64 per pound would be (20 - x) pounds, as the total weight of the mixture is 20 pounds.
To find the total cost of the candy worth $3.46 per pound, we multiply the weight (x) by the cost ($3.46) per pound, giving us 3.46x dollars.
The total cost of the candy worth $1.64 per pound would be (20 - x) pounds times $1.64 per pound, which is 1.64(20 - x) dollars.
To find the total cost of the mixture, we multiply the weight (20 pounds) by the cost ($3.00) per pound, giving us 3.00(20) = 60 dollars.
Since the total cost of the mixture is the sum of the costs of the two types of candy, we have the equation:
3.46x + 1.64(20 - x) = 60
Simplifying this equation, we can distribute 1.64 into the parentheses:
3.46x + (32.8 - 1.64x) = 60
Next, we combine like terms:
3.46x - 1.64x + 32.8 = 60
Now, we combine the x terms:
1.82x + 32.8 = 60
Subtract 32.8 from both sides:
1.82x = 27.2
Finally, divide both sides by 1.82 to solve for x:
x = 27.2 / 1.82 = 15
So, Ellen should use 15 pounds of the candy worth $3.46 per pound.
To find out how many pounds of the more expensive candy Ellen should use, we can set up a system of equations based on the given information.
Let's assume that Ellen uses x pounds of the candy worth $3.46 per pound. Since she wants to form a 20-pound mixture, she would then use (20 - x) pounds of the candy worth $1.64 per pound.
The cost of the more expensive candy will be the product of its price per pound ($3.46) and the amount used (x). The cost of the cheaper candy will be the product of its price per pound ($1.64) and the amount used (20 - x). Since we want the total cost of the mixture to be $3.00 per pound, we can set up the equation:
(3.46 * x) + (1.64 * (20 - x)) = 3.00 * 20
Simplifying this equation, we get:
3.46x + 32.80 - 1.64x = 60
Combining like terms, we have:
1.82x + 32.80 = 60
Subtracting 32.80 from both sides of the equation, we get:
1.82x = 27.20
Dividing both sides of the equation by 1.82, we find:
x = 15
Therefore, Ellen should use 15 pounds of the candy worth $3.46 per pound.