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# Scale, Rates, and Simple Interest Study Guide for GED Math

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Updated on Jan 14, 2011

Practice problems for these concepts can be found at:

Measurement Practice Problems for GED Math

### Scale

Scale is a special ratio used for models of real-life items, such as model railroads and model airplanes, or scale drawings such as blueprints and maps. On model airplanes, you will often find the scale ratio printed on the model as model:real. For example, a toy car may have the ratio 1:62 printed on the bottom. This is the ratio of all of the dimensions of the toy to the corresponding dimensions of the real car. This scale ratio says that the real car is 62 times larger than the toy, since the ratio is 1:62.

Example

A model locomotive measures 8.7 inches in length. If the scale given is 1:16, how long is the real locomotive?

Because the real train engine is 16 times as big as the model, the real train engine will be 8.7 times 16, which is 139.2 inches, or 11.6 feet.

On scale drawings, the scale will be a comparison of a small distance unit, like inches, to a large distance unit, like feet or even miles. So a scale on a map could read "3 inches = 10 miles." This means for every 3 inches on the map, the actual distance is 10 miles. This ratio is , but care should be taken to remember that the units do not agree. If a scale drawing reads "1 inch = 10 feet," this does not mean that the real item is only 10 times bigger, even though the ratio would be 1:10. Solve scale drawing problems as you would any type of ratio problem, keeping the units consistent and clear in your answer.

### Rates

A rate is a ratio that compares two different units of measurement. It is usually written as a fraction with a denominator of 1. Sometimes, the word per is used to indicate a rate. Per means for each (for 1). For example, a rate of \$0.99 per minute is written \$0.99/1 minute. (Notice that the units for this rate are dollars and minutes.)

Some common rates include the following:

Rate problems can be solved by writing a proportion. Suppose the price of five pounds of grapes is \$3.50. What is the price of three pounds of grapes?

price/pound = \$3.50/5 pounds = ?/3 pounds
Solve for ? by cross multiplying:
5 × ? = \$3.50 × 3
5 × ? = \$10.50

Divide each side of the equation by 5.

### Calculating Simple Interest

Interest is the amount of money that is paid for using someone else's money. For example, a bank pays you interest for money you have placed in a savings account. Or, you pay a bank interest for money that you borrow.

Here is the interest formula:

interest = principal × rate × time

Suppose you put \$500 in a savings account that pays 5% simple interest each year. How much interest will you have earned in 18 months?

interest = \$500 × 5% × 18 months

The rate (5%) can be written as a decimal or a fraction: 0.05 or , which reduces to .

interest = \$500 × × 18 months

Because the rate is a yearly rate, write 18 months as a number of years: 18 months = years, which reduces to years.

Practice problems for these concepts can be found at:

Measurement Practice Problems for GED Math