scale factor problem

[Genisnotme]

You are drawing a scale model of a rectangular swimming pool on a piece of 8.5 inch by 11 inch paper. The pool is 50 ft long and 20 ft wide. What is the largest scale ( as in : ft ) you could choose that will still fit on the paper so that the dimensions of the pool will be a whole number of inches?

 

[Dr.Peterson]

You are drawing a scale model of a rectangular swimming pool on a piece of 8.5 inch by 11 inch paper. The pool is 50 ft long and 20 ft wide. What is the largest scale ( as in : ft ) you could choose that will still fit on the paper so that the dimensions of the pool will be a whole number of inches?

First find the largest scale such that the longer dimension, 50 ft, will fit the the largest whole number of inches in the long dimension of the paper (8 in). Will the width fit? Then do the same starting with the width, and see if the long dimension will fit. There may be more work to do to get both dimensions to be whole numbers.

If you're having trouble, please show what you've done so we can guide you. I can see several places where you might be stuck. You can be assured this is not a problem I can just look at and say what formula to use! You have to be willing to try things.

 

[JeffM]

[MATH]0 < a < 8.5 \text { and } 0 < \dfrac{50a}{20} < 11 \text { and } a \text { and } \dfrac{50a}{20} \in \mathbb Z^+[/MATH].

[MATH]a \ge 5 \implies \dfrac{50a}{20} \ge 12.5 \not \le 11.[/MATH]
[MATH]\therefore a = 4 \implies \dfrac{50a}{20} = 10.[/MATH]
[MATH]\dfrac{20}{4} = 5.[/MATH]
Therefore, scaling at 1 inch for 5 feet will show a pool with a width of 20 ft and a length of 50 ft as 4 inches by 10 inches, which comfortably fits on 8.5 x 11 paper.