Praxis Core Academic Skills for Educators: Mathematics (5733)Number and QuantityMedium
A cartographer is scaling a map. A distance of 1.5 inches on the map represents an actual distance of 30 miles. If two cities are 4.2 inches apart on the map, what is the actual distance between them?
- A96 miles
- B84 miles
- C63 miles
- D72 miles
Show answer & explanationAnswer & explanation
Correct answer: B. 84 miles
This is a proportion problem. Set up the ratio: 1.5 inches / 30 miles = 4.2 inches / x miles. Cross-multiply: 1.5 * x = 30 * 4.2. 1.5x = 126. Divide both sides by 1.5: x = 126 / 1.5 = 84 miles.
Why the other options are wrong
- A. This might result from a calculation error or incorrect setup of the proportion.
- C. This might result from a calculation error or incorrect setup of the proportion, perhaps using 1.5 * 4.2.
- D. This might result from a calculation error or incorrect setup of the proportion.
Solving Proportions
A proportion is an equation stating that two ratios are equal. To solve for an unknown in a proportion, use cross-multiplication: multiply the numerator of one ratio by the denominator of the other, and set the products equal.
- Set up two equal ratios.
- Cross-multiply the terms.
- Solve the resulting linear equation for the unknown variable.
Memory trick: Ratios equal, cross-multiply, then solve for the unknown guy!