A gardener planted 14 flats of flowers, filling 2/3 of a garden. How many flats would fill the whole garden?

1. Let g be the number of flats that fill the whole garden. 2. Two-thirds of the whole garden took 14 flats, so (2/3)g = 14. 3. Multiply both sides by the reciprocal 3/2: g = 14 x 3/2. 4. Multiply: 14 x 3 = 42 flats, then divide by 2: g = 21. 5. So 21 flats would fill the whole garden. 6. Check: 2/3 of 21 flats is 14 flats, matching what was planted. 7. 9 flats is the trap of taking 2/3 of 14, and 28 flats doubles 14 as if half the garden had been planted rather than two-thirds. _Source: OpenStax Elementary Algebra (CC BY 4.0), Ch 2 "Solving Linear Equations and Inequalities", section 2.2 Solve Equations using the Division and Multiplication Properties of Equality_