similiar shapes

Question

on a map 1/4 inch represents 350 miles how long would a line on a map need to be in order to represent 3200 miles

Answer 1

We can set up a proportion to help solve this problem. We know for each additional 1/4 inch on the map, another 350 miles is covered in real life, so 1/4 inch : 350 miles is our ratio. Another way to write this is

1/4 inch

________________________

350 miles

This ratio is constant regardless of how many miles covered. Therefore the ratio can be set equal to :

1/4 inch. x inches

_____________ = ___________

350 miles. 3200 miles

This equation will tell us how many inches on the map are needed for 3200 miles to guarantee the ratio of x : 3200 is equivalent 1/4 : 350.

If we multiply both sides of the equation by 3200, we end up with

3200*1/4

___________ = x

350

Simplifying this, x ≈ 2.286 inches.

Therefore, 3200 miles would be represented on the map with a line that was approximately 2.286 inches long.

I hope this helps. Please let me know if you have any questions regarding this answer or any other questions in general

Answer 2

1/4 in proportion to 350

equals

x in proportion to 3200

cross multiplies:

(1/4) * 3200 = 350 * x

800 = 350 * x

x = 800/350 = 2 and 100/350 = 2 and 2/7 inches

Answer 3

Kelvin,

This is a proportion problem, and you set up up as two ratios that are equal to each other.

The first ratio is 1/4 / 350

The second ratio is x / 3200

Ser the equal to each other, cross multiply, and solve for the variable x. It looks like this:

1/4 / 350 = x / 3200

350x = 800

x = 2.285 rounded to 2.29