Let's define the problem step by step.
Given:
- Two coffee grades:
- Grade A: $0.33 per pound
- Grade B: $0.24 per pound
- Initial mixture ratio: 2 parts Grade A to 1 part Grade B
- New mixture ratio: 1 part Grade A to 2 parts Grade B
- Total weight to blend: 100 pounds
Step 1: Calculate cost per pound of the initial mixture.
- Total parts in the initial mix = 2 + 1 = 3 parts
- Weight of Grade A in initial mix per pound = 2/3 pound
- Weight of Grade B in initial mix per pound = 1/3 pound
Cost of 1 pound of initial blend = (2/3 × $0.33) + (1/3 × $0.24)
= $0.22 + $0.08 = $0.30 per pound
Step 2: Calculate cost per pound of the new mixture.
- Total parts in the new mix = 1 + 2 = 3 parts
- Weight of Grade A in new mix per pound = 1/3 pound
- Weight of Grade B in new mix per pound = 2/3 pound
Cost of 1 pound of new blend = (1/3 × $0.33) + (2/3 × $0.24)
= $0.11 + $0.16 = $0.27 per pound
Step 3: Calculate total cost for 100 pounds in each case.
- Initial cost = 100 × $0.30 = $30.00
- New cost = 100 × $0.27 = $27.00
Step 4: Calculate savings.
Savings = Initial cost - New cost = $30.00 - $27.00 = $3.00
Answer:
The shop will save $3.00 by changing the blend ratio on 100 pounds of coffee.
