2. How many pounds of chocolate worth $1.20 a pound must be mixed with 10 pounds of chocolate worth 90 cents a pound to produce a mixture worth $1.00 a pound?
What Do I Know?
What Do I Want to Know?
Assign Variables
Write a verbal Model:
How Do I Find the Components of the Verbal Model?
Write an Algebraic Equation
Solve
Write Your Summary Statement
What Do I Know?
You know the cost per pound of two types of chocolate: $1.20 per pound and $0.90 per pound. You also know the desired cost per pound of the resulting mixture, which is $1.00 per pound. Additionally, you know the amount of one type of chocolate, which is 10 pounds.
What Do I Want to Know?
You want to know how many pounds of the $1.20 per pound chocolate must be mixed with the 10 pounds of $0.90 per pound chocolate to produce a mixture worth $1.00 per pound.
Assign Variables:
Let's assign a variable to the unknown quantity we want to find. Let's say x represents the number of pounds of the $1.20 per pound chocolate.
Write a Verbal Model:
To solve this problem, we can set up the following verbal model: The total cost of the $1.20 per pound chocolate plus the total cost of the $0.90 per pound chocolate should equal the total cost of the mixture.
How Do I Find the Components of the Verbal Model?
To find the components of the verbal model, we need to determine the cost of each chocolate type. The cost of the $1.20 per pound chocolate can be found by multiplying the cost per pound ($1.20) by the number of pounds (x). The cost of the $0.90 per pound chocolate is already given as $0.90 per pound, and we know the number of pounds is 10.
Write an Algebraic Equation:
Using the components from the verbal model, we can write the algebraic equation: 1.20x + 0.90(10) = 1.00(x + 10)
Solve:
Now we can solve the equation to find the value of x.
1.20x + 9 = 1.00x + 10
0.20x = 1
x = 5
Write Your Summary Statement:
To produce a mixture worth $1.00 per pound, you would need to mix 5 pounds of the $1.20 per pound chocolate with the 10 pounds of $0.90 per pound chocolate.