Math Problem Statement

The scale on a map is drawn so that 3.5 inches corresponds to an actual distance of 175 miles. If two cities are 7.75 apart on the map, how many miles apart are they? (round to the nearest tenth)

Solution

The scale provided indicates that 3.5 inches on the map corresponds to 175 miles in actual distance. To solve this problem, we will set up a proportion based on the scale and use it to find the actual distance between the two cities that are 7.75 inches apart on the map.

  1. Set up the proportion:

[ \frac{3.5 \text{ inches}}{175 \text{ miles}} = \frac{7.75

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Math Problem Analysis

Mathematical Concepts

Ratios
Proportions
Linear Scaling

Formulas

(Map distance / Actual distance) = (New map distance / New actual distance)

Theorems

Proportion Theorem

Suitable Grade Level

Grades 6-8

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