Final answer:
To fulfill the condition of two proportions with the product of the means equaling 27, one could use 9 inches/1 inch = 3 inches/1 inch and 27 feet/1 foot = 1 foot/1 foot as examples, both meeting this criterion.
Step-by-step explanation:
To write two proportions so that the product of the means equals 27, you can set up two ratios where the means (the middle terms when the proportions are written in fraction form) multiply to give 27. A proportion is a statement that two ratios are equal.
For example:
- Let's consider the first proportion. Assume we have lengths in inches, and we set up the ratio 9 inches/1 inch because 9 times 3 equals 27. Our second term will be 3 inches/1 inch to complete the first proportion.
- As for the second proportion, let's use widths in feet. We could have a ratio like 27 feet/1 foot, since 27 times 1 equals 27. The second term here would be 1 foot/1 foot.
These two examples give us our two proportions:
- 9 inches/1 inch = 3 inches/1 inch (9 x 3 = 27)
- 27 feet/1 foot = 1 foot/1 foot (27 x 1 = 27)
Both proportions meet the condition where the product of the means equals 27.