Final answer:
Jayden mistakenly thought two scales were different, but 1 inch to 12 inches and 1 inch to 1 foot are equivalent as 1 foot is 12 inches. Scale factor is key in converting actual measurements to scale measurements and vice versa.
Step-by-step explanation:
Jayden is incorrect about Kimberly and Claire using the same scale. Although it may seem at a glance that 1 inch to 12 inches and 1 inch to 1 foot are equivalent, they are fundamentally different because 1 foot equals 12 inches. Therefore, both scales actually describe the same proportional relationship.
Understanding scale factor is also crucial when solving problems related to scale drawings and models. For example, with a scale of 1 inch = 6 feet, a 30-foot-tall school building would be 5 inches tall in the model because 30 feet divided by 6 feet per inch equals 5 inches.
Similarly, if the width of the building is 120 feet, the scale model width would also be calculated by dividing 120 feet by the scale factor, resulting in a model width of 20 inches. When converting actual measurements to scale measurements or vice versa, division or multiplication by the scale factor, which is derived from the scale, is essential for accurate representation.