Sweet job wants to sell special mix that consists of 18 pounds of dark chocolate worth seven dollars a pound and milk chocolate worth $5.50 a pound she wants to sell the special mix for six dollars a pound how many pounds of milk chocolate should be added to the dark chocolate

Answer 1

To solve the problem, we need to set up an equation based on the values given.

Let \( x \) be the number of pounds of milk chocolate that should be added to the 18 pounds of dark chocolate.

1. The weight of the dark chocolate is 18 pounds.
2. We are adding \( x \) pounds of milk chocolate.
3. The total weight of the mixture will then be \( 18 + x \) pounds.
4. The price per pound of dark chocolate is $7, and for milk chocolate, it is $5.50. The selling price for the mixture is $6 per pound.

Now, we can set up the equation based on the total value of the chocolates:

The total value of the dark chocolate is: \[ 18 \text{ pounds} \times 7 \text{ dollars/pound} = 126 \text{ dollars} \]

The total value of the milk chocolate is: \[ x \text{ pounds} \times 5.50 \text{ dollars/pound} = 5.5x \text{ dollars} \]

The total value of the mixture (when sold at $6 per pound) is: \[ (18 + x) \text{ pounds} \times 6 \text{ dollars/pound} = 108 + 6x \text{ dollars} \]

Setting up the equation for the total value: \[ 126 + 5.5x = 108 + 6x \]

Now, solve for \( x \):

1. Subtract \( 5.5x \) from both sides: \[ 126 = 108 + 0.5x \]

2. Subtract 108 from both sides: \[ 18 = 0.5x \]

3. Multiply by 2 to solve for \( x \): \[ x = 36 \]

Conclusion: To create the special mix, Sweet Job should add 36 pounds of milk chocolate to the 18 pounds of dark chocolate.