Alandscape designer has a drawing of a flower bed that measures 6 inches by 9 inches. the owner wants the actual flower bed to be 5 feet by 7.5 feet. what is the scale factor the designer must use to install the new flower bed ?

Under given circumstances, we have two ratios: 6:5 and 9:7.5. We can clearly see that 5 is 5/6 of 6. The question is: is 7.5 also 5/6 of 9? Let's check it:

9 * 5/6 =
= 45/6 =
= 7 3/6 =
= 7 1/2 =
= 7.5

It's correct. It means that the designer has to use a scale of 5/6 in comparison to the real dimensions.