Final answer:
To create a 100 lb blend of chocolate at $15/lb using chocolates that cost $16/lb and $12/lb, the master chocolatier should use 75 lbs of the $16/lb chocolate and 25 lbs of the $12/lb chocolate.
Step-by-step explanation:
The student's question pertains to a blend of two types of chocolates, one costing $16/lb and the other $12/lb, to create a 100 lb mixture that costs $15/lb. This is a typical algebra problem that can be solved using a system of equations to find the quantity of each type of chocolate to blend.
Step-by-Step Solution:
1. Let x be the amount of the $16/lb chocolate and y be the amount of the $12/lb chocolate.
2. The first equation comes from the total weight of the blend: x + y = 100 lbs.
3. The second equation comes from the total cost of the blend: 16x + 12y = 15 × 100.
4. Solving these equations simultaneously, we can either use substitution or elimination methods to find the values of x and y.
5. Using elimination, we can multiply the first equation by 12 to get 12x + 12y = 1200.
6. Now we subtract the new first equation from the second equation: (16x + 12y) - (12x + 12y) = 1500 - 1200, which simplifies to 4x = 300.
7. Dividing by 4 we find x = 75. Substituting x into the first equation, 75 + y = 100, we find that y = 25.
Thus, the master chocolatier should mix 75 lbs of the $16/lb chocolate with 25 lbs of the $12/lb chocolate to create the desired 100 lb blend at $15/lb.