If the distance from your dorm to the location of your first class is 10.5 inches on this map, do you have to walk more than a mile or less than a mile to get to your first class? By how much?

Question

The scale on a campus map states that 1 inch represents 500 feet.

Is it less than or more than 30 feet?

Answer 1

Hi Shanti,

If 1 inch = 500 feet, you can set up a proportion to solve:

1 = 10.5

500 x

Then cross multiply to solve. This will get you how many feet are needed. Then compare that number to 1 mile which is 5280 feet and see if it is more or less.

Thanks!

Answer 2

Before we convert to miles, let's solve the second part "is it less or more than 30 feet?"

1. This can be solved using proportions
2. In words, 1 inch is to 500 feet as 10.5 inches is to _ feet
3. Algebraically, (1/500) = (10.5/x)
4. (1/500)*x = (10.5/x)*x
5. (x/500) = 10.5
6. (x/500)*500 = 10.5*500
7. x = 5,250 feet
8. So, we have proven the distance is substantially larger than 30 feet
9. Now, recall that 1 mile is equal to 5,280 feet
10. Proportionally, 1 mile is to 5,280 feet as _ miles is to 5,250 feet
11. Algebraically, (1/5280) = (x/5250)
12. (1/5280)*5250 = (x/5250)*5250
13. (5250/5280) = x
14. x = (175/176) miles = 0.99432 miles < 1 mile
15. Therefore, the distance from your dorm to your class is less than a mile by 1/176 of a mile or approximately 0.00568 miles

Answer 3

1 inch represents 500 feet.

10.5 inches =10.5 *500=5250 feet

1 mile = 5280 feet

so you have to walk less than a mile