Helpers are needed to prepare cakes in a bakery. Each helper can make either 2…

Concept: When one helper can produce two different items at two different rates, convert every requirement into a common unit — helper-hours, the time one helper alone would need to make that quantity. The number of helpers required equals the total helper-hours needed divided by the number of hours actually available.

1. Large cakes: one helper makes 2 large cakes per hour, so producing 20 large cakes needs 20 ÷ 2 = 10 helper-hours.

2. Small cakes: one helper makes 35 small cakes per hour, so producing 700 small cakes needs 700 ÷ 35 = 20 helper-hours.

3. Total work required = 10 + 20 = 30 helper-hours.

4. The kitchen is available for 3 hours, so the number of helpers needed = total helper-hours ÷ hours available = 30 ÷ 3 = 10.

Cross-check: In the half hour it takes to make one large cake (at 2 per hour), a helper could instead make 35 × 0.5 = 17.5 small cakes, so one large cake is worth 17.5 small-cake-equivalent units of work. The 20 large cakes then equal 20 × 17.5 = 350 such units, giving a combined total of 350 + 700 = 1050 units. Each helper, working the full 3-hour shift at 35 small cakes per hour, contributes 3 × 35 = 105 units, so the number of helpers required = 1050 ÷ 105 = 10 — matching the first method and confirming the answer.