Quality control on garments: sleeve and body alterations across 60 shirts Every 2 out of 3 shirts need sleeve alterations and every 4 out of 5 need body alterations. For 60 shirts, how many total alterations are required (counting sleeve and body as separate alterations)?

Introduction / Context:
Garment alteration planning often tracks different alteration types separately. Here, sleeve and body alterations have different rates. The question asks for the total number of alterations, not the number of shirts.

Given Data / Assumptions:

• Total shirts = 60.
• Sleeve alterations needed in 2 out of 3 shirts.
• Body alterations needed in 4 out of 5 shirts.
• Each alteration type is counted once per shirt (if needed).

Concept / Approach:
Compute the count for each alteration type independently using the given fractions, then sum them. Shirts needing both contribute 2 alterations to the total.

Step-by-Step Solution:

Verification / Alternative check:
Whether or not some shirts overlap does not matter since the question counts alterations, not altered shirts. Overlap only affects how many shirts are touched, not the sum of alteration operations.

Why Other Options Are Wrong:

• 123, 133, 143: These would require different rates or double-counting errors.

Common Pitfalls:
Interpreting the problem as asking for number of shirts altered at least once, or subtracting the overlap. The prompt clearly wants total operations.

Final Answer:
88