Cake pieces and weight — a cake is cut into two halves; one half is cut into equal small pieces of 20 g each. If she has 7 pieces total (including the uncut half), what was the weight of the original cake?

Introduction / Context:
This partition-and-weight problem uses careful interpretation of “pieces.” One half of the cake remains as a single large piece; the other half is subdivided into equal 20 g pieces. The total number of pieces in hand is 7, which helps deduce how many small pieces were cut and thus the cake’s total mass.

Given Data / Assumptions:

• The cake is divided into two equal halves.
• One half remains intact as one large piece.
• The other half is cut into equal small pieces, each 20 g.
• Total pieces in hand = 7 (i.e., 1 large half + small pieces).

Concept / Approach:
From the piece count, infer how many small pieces exist. Then compute the weight of that cut half. Double it to find the whole cake’s weight because both halves are equal.

Step-by-Step Solution:

Verification / Alternative check:
If the cake weighed 240 g, each half is 120 g. Cutting one half into six pieces of 20 g each produces exactly 6 small pieces; along with the other intact half, total pieces = 7. All conditions satisfied.

Why Other Options Are Wrong:

• 120 g, 140 g, 280 g — do not reconcile with 6 equal 20 g small pieces plus one intact half.
• None of these — incorrect because 240 g fits perfectly.

Common Pitfalls:
Miscounting the intact half as multiple pieces or assuming both halves are subdivided. Only one half is cut into small pieces; the other remains one piece.

Final Answer:
240 grams