Question

one chocolate costs $16/lb and other chocolate costs $12/lb. The master chocolatier ants you to blend 100lb of the two chocolates together will cost $15/lb. How much of each chocolate should you use ? math

Answer 1

To blend two types of chocolate to cost $15 per pound, the chocolatier should use 75 pounds of the $16 chocolate and 25 pounds of the $12 chocolate, which can be determined by solving a system of equations.

Step-by-step explanation:

To solve the problem of blending two chocolates to achieve a certain price per pound, we can set up a system of equations based on the prices and weights of the chocolates.

Let's denote x as the amount (in pounds) of the $16 chocolate and y as the amount (in pounds) of the $12 chocolate. Since we want a total of 100 pounds, we can write the first equation as:

x + y = 100

We also need the total cost of the 100 pounds of mixed chocolate to equal $15 per pound, which gives us our second equation. The total cost of x pounds of $16 chocolate is 16x, and for y pounds of $12 chocolate it is 12y. So:

16x + 12y = 15 × 100

We can now solve this system of equations. First, solve the first equation for x:

x = 100 - y

Substitute x in the second equation:

16(100 - y) + 12y = 1500

Multiply out the terms:

1600 - 16y + 12y = 1500

Combine like terms:

1600 - 4y = 1500

Solve for y:

4y = 100

y = 25

Now, substitute y back into the equation x = 100 - y:

x = 100 - 25

x = 75

Therefore, the chocolatier should use 75 pounds of the $16 chocolate and 25 pounds of the $12 chocolate to create 100 pounds of a blend costing $15 per pound.