What is the ratio of the number of American hotcakes sold by bakery C to the…

Concept

A total that is split into exactly three varieties is fully determined once any two of the three counts are known. Each row here supplies one variety's count together with the size of the gap between a second variety and that first one; because the accompanying note fixes which member of that pair is larger, the gap is added to the given count to recover the second variety, and the third variety is whatever the row total still leaves. A ratio of two such recovered counts is then written in the order the question asks and reduced by their highest common factor.

Applying it here

1. Bakery C sells 360 Cornmeal hotcakes, and the gap between its American and Cornmeal counts is 80. Note (2) fixes American as the larger member of that pair, so the gap is added: American at C = 360 + 80 = 440.

2. Bakery D sells 420 Cornmeal hotcakes with a gap of 40, so by the same reasoning American at D = 420 + 40 = 460.

3. Note (1) makes the three varieties add up to the row total, so Swedish at D = 1320 - 420 - 460 = 440.

4. The question asks for American at bakery C compared with Swedish at bakery D, in that order: 440 : 440. Dividing both terms by their highest common factor, 440, gives 1 : 1.

Cross-check

Recovering bakery C's Swedish count the same way gives 1000 - 360 - 440 = 200, so each bakery's three varieties add back to its stated total: 360 + 440 + 200 = 1000 for C and 420 + 460 + 440 = 1320 for D. In both rows the American count comes out larger than the Cornmeal count, exactly as Note (2) requires. Had the stated gap been subtracted instead of added, American would have fallen below Cornmeal and broken that note, so addition is the step the data supports.