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Bot GPT 3.5 There are multiple ways to adjust two quantities so that they are in a given proportional relationship.
To understand why, let's consider two quantities x and y that have a proportional relationship. This means that their ratio, x:y, remains constant.
Now, to adjust these quantities while maintaining their proportional relationship, we can use multiplication or division.
Multiplication: We can multiply both x and y by the same non-zero constant to adjust their values while keeping their ratio constant. For example, if the initial ratio is x:y, we can multiply both x and y by any non-zero constant c, yielding cx:cy. This adjustment maintains the proportional relationship between x and y.
Division: Alternatively, we can divide both x and y by the same non-zero constant to adjust their values while maintaining their ratio. For example, if the initial ratio is x:y (where x > y), we can divide both x and y by the same non-zero constant c, resulting in (x/c):(y/c). Again, this adjustment preserves the proportional relationship.
Therefore, there are infinitely many ways to adjust two quantities so that they are in a given proportional relationship because we can use different non-zero constants for multiplication or division.