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

What Do I Know?

You know the prices per pound for two types of chocolate and the desired price per pound for the mixture. You also know the amount of one type of chocolate that is already available.

What Do I Want to Know?
You want to know how many pounds of the other type of chocolate should be mixed with the given amount of chocolate to produce a mixture with the desired price per pound.

Assign Variables:
Let's assign the following variables:
- x: the number of pounds of chocolate worth $1.20 per pound that need to be mixed
- 10: the amount in pounds of chocolate worth 90 cents per pound that is already available
- $1.20: the price per pound for chocolate worth $1.20 per pound
- $0.90: the price per pound for chocolate worth $0.90 per pound
- $1.00: the desired price per pound for the mixture

Write a Verbal Model:
The verbal model for this problem can be written as follows:
"The total value of chocolate worth $1.20 per pound plus the total value of chocolate worth $0.90 per pound should equal the total value of the mixture, with the total weight of chocolate equal to the sum of the weights of the individual chocolates."

How Do I Find the Components of the Verbal Model?
To find the components of the verbal model, we need to consider the value of each type of chocolate.

The value of 10 pounds of chocolate worth 90 cents per pound is calculated as follows:
10 pounds * $0.90/pound = $9

The value of x pounds of chocolate worth $1.20 per pound is calculated as follows:
x pounds * $1.20/pound = $1.20x

Therefore, the equation for the verbal model is:
$9 + $1.20x = $1.00 * (10 + x)

Write an Algebraic Equation:
The equation for the verbal model can be written as:
9 + 1.20x = 1.00 * (10 + x)

Solve:
To solve the equation, we can begin by distributing the 1.00 on the right side:
9 + 1.20x = 10 + 1.00x

Next, we can simplify the equation by combining like terms:
0.20x = 1

To isolate the variable x, we will divide both sides of the equation by 0.20:
x = 1/0.20

Evaluating the expression on the right:
x = 5

Therefore, you need to mix 5 pounds of chocolate worth $1.20 per pound with the 10 pounds of chocolate worth $0.90 per pound to produce a mixture worth $1.00 per pound.