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4.16: Use Metric and Customary Units of Measurement in Problem Solving

Difficulty Level: At Grade Created by: CK-12
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Practice Conversion of Systems of Measure

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Omar’s dog, Harry, is a Golden Retriever and weighs 30 pounds. How can Omar figure out Harry’s weight in kilograms?

In this concept, you will learn to use metric and customary units of measurement in problem solving.

Measurement Conversions

Sometimes it is necessary to convert between customary and metric units of measurements. These measurement conversions will be estimates, because you cannot make an exact measurement when converting between systems of measurement.

Measurement Conversions

Let’s look at an example.

Randy ran a 20 kilometer race. How many miles did Randy run?

First, set up a proportion.

1 mi1.6 km=x mi20 km\begin{align*}\frac{1 \ mi}{1.6 \ km} = \frac{x \ mi}{20 \ km} \end{align*}

Next, cross multiply.

11.61.6x1.6x===x201×2020\begin{align*} \begin{array}{rcl} \frac{1}{1.6}&=& \frac{x}{20} \\ 1.6x&=&1 \times 20 \\ 1.6x&=&20 \end{array}\end{align*}

Then, divide both sides by 1.6 to solve for x\begin{align*}x\end{align*}.

1.6x1.6x1.6x===20201.612.5\begin{align*} \begin{array}{rcl} 1.6x&=&20 \\ \frac{1.6x}{1.6}&=& \frac{20}{1.6} \\ x&=&12.5 \end{array} \end{align*}The answer is 12.5.

Randy ran 12.5 miles.

Examples

Example 1

Earlier, you were given a problem about Omar and his dog Harry.

Omar wants to know how many kilograms Harry weighs knowing that his weight in pounds is 30.

First, set up a proportion.

1 lb0.454 kg=30 lbx kg\begin{align*}\begin{array}{rcl} \frac{1 \ lb}{0.454 \ kg}&=& \frac{30 \ lb}{x \ kg} \end{array}\end{align*}

Next, cross multiply to solve for x\begin{align*}x\end{align*}.

10.4541xx===30x30×0.45413.62\begin{align*}\begin{array}{rcl} \frac{1}{0.454}&=& \frac{30}{x} \\ 1x&=&30 \times 0.454 \\ x&=&13.62 \end{array}\end{align*}

The answer is 13.62.

Harry weighs approximately 13.6 kg.

Example 2

How many meters are in 67 feet?

First, set up a proportion.

1 ft0.30 m=65 ftx m\begin{align*}\frac{1 \ ft}{0.30 \ m}= \frac{65 \ ft}{x \ m} \end{align*}

Next, cross multiply to solve for x\begin{align*}x\end{align*}.

10.31xx===65x0.3×6519.5\begin{align*}\begin{array}{rcl} \frac{1}{0.3}&=& \frac{65}{x} \\ 1x&=& 0.3 \times 65 \\ x&=&19.5 \end{array} \end{align*}The answer is 19.5.

Therefore 65 feet is approximately 19.5 meters.

Example 3

John ran 5 kilometers. How many miles did he run?

First, set up a proportion.

1 mi1.6 km=x mi5 km\begin{align*}\frac{1 \ mi}{1.6 \ km} = \frac{x \ mi}{5 \ km}\end{align*}Next, cross multiply.

11.61.6x1.6x===x51×55\begin{align*}\begin{array}{rcl} \frac{1}{1.6}&=& \frac{x}{5} \\ 1.6x&=& 1 \times 5 \\ 1.6x&=&5 \end{array}\end{align*}

Then, divide both sides by 1.6 to solve for x\begin{align*}x\end{align*}.

1.6x1.6x1.6x===  551.63.125\begin{align*}\begin{array}{rcl} 1.6x &=& \ \ 5 \\ \frac{1.6x}{1.6} &=& \frac{5}{1.6} \\ x &=& 3.125 \end{array}\end{align*}

The answer is 3.125.

Therefore, 5 kilometers is approximately 3.1 miles.

Example 4

Kary measured out 12 inches on a ruler. About how many centimeters would that be?

First, set up a proportion.

1 in2.54 cm=12 inx cm\begin{align*}\frac{1 \ in}{2.54 \ cm} = \frac{12 \ in}{x \ cm} \end{align*}Next, cross multiply.

12.541xx===12x12×2.5430.48\begin{align*}\begin{array}{rcl} \frac{1}{2.54} &=& \frac{12}{x} \\ 1x &=& 12 \times 2.54 \\ x &=& 30.48 \end{array}\end{align*}

The answer is 30.48.

Therefore, 12 inches is approximately 30.5 centimeters.

Example 5

Sandy ran 15 meters. About how many feet is that?

First, set up a proportion.

1 ft0.30 m=x ft15 m\begin{align*}\frac{ 1 \ ft}{0.30 \ m} = \frac{x \ ft}{15 \ m} \end{align*}

Next, cross multiply.

10.30.3x0.3x===x151×1515\begin{align*}\begin{array}{rcl} \frac{1}{0.3}&=& \frac{x}{15} \\ 0.3x&=&1 \times 15 \\ 0.3x&=&15 \end{array}\end{align*}

Then, divide both sides by 0.3 to solve for x\begin{align*}x\end{align*}.

0.3x0.3x0.3x===15150.350\begin{align*}\begin{array}{rcl} 0.3x &=& 15 \\ \frac{0.3x}{0.3} &=& \frac{15}{0.3} \\ x &=& 50 \end{array}\end{align*}

The answer is 50.

Therefore, 15 meters is approximately 50 feet.

Review

Answer each question by using benchmarks.

1. About how many centimeters is in one inch?
2. About how many centimeters is in three inches?
3. About how many inches is in 5 centimeters?
4. About how many centimeters is in 1 foot?
5. About how many centimeters is in 3 feet?
6. About how many centimeters is in 1 yard?
7. About how many meters are there in one yard?
8. About how many meters are there in three yards?
9. About how many yards are there in twenty -four meters?
10. About how many feet are there in eighteen meters?
11. About how many kilometers are there in 1.8 miles?
12. About how many miles are there in 10 kilometers?
13. About how many miles are there in 30 kilometers?
14. About how many miles are there in 15 kilometers?
15. About how many kilometers are there in 10 miles?

To see the Review answers, open this PDF file and look for section 4.16.

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Vocabulary Language: English

Customary System

The customary system is the measurement system commonly used in the United States, including: feet, inches, pounds, cups, gallons, etc.

Metric System

The metric system is a system of measurement commonly used outside of the United States. It contains units such as meters, liters, and grams, all in multiples of ten.

Proportion

A proportion is an equation that shows two equivalent ratios.

Ratio

A ratio is a comparison of two quantities that can be written in fraction form, with a colon or with the word “to”.

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