## Pages

### Scale two units of measurement

Scale two units of measurement

On a map every 50 miles is represented as 0.2 centimeters. How many miles is 1.5 centimeters on the map?
The two units of measurement are miles and centimeters.
Set up a proportion for miles and centimeters. Let the unknown miles be 𝒙.
$$\boldsymbol{\frac {miles}{centimeters}=\frac {50}{0.2}=\frac {x}{1.5}}$$
Cross multiply and solve for 𝒙.
0.2 × 𝒙  =  1.5 × 50
0.2𝒙  =  75
𝒙  =  375 miles
When setting up a proportion, it is important to have the same units in numerator and denominator.

Explanation on proportion:
In the above example, it is given that 50 miles is 0.2 centimeters. This means that for any given value of miles or centimeters, the ratio of miles:centimeter will always be 50:0.2. Hence,
miles:centimeter  =  50:0.2  =  unknown miles:1.5
Proportion is a ratio written as a fraction. Similar ratios can be equated as fractions as shown in the solution above.

Try the following:
1.  A building architect has created a scale for the height of a building. On the scale 30 feet is represented as 2 inches. How many inches represent 720 feet on the architect's scale?
2.  Tara is planning to drive to her cousin's house. On a map the distance between Tara and her cousin's home is 18 centimeters. If 0.4 centimeters on the map represents 3 miles, how many miles will Tara drive from her home to her cousin's home?
3.  A small city has two large shopping malls. On the city map the distance between the two shopping malls is 3 inches. If 0.15 inches on the map corresponds to 10 miles, how far apart are the two shopping malls in miles?

1.  $${\frac {inches}{feet}=\frac {2}{30}=\frac {x}{720} → {x=48}\ {inches}}$$
2.  $${\frac {miles}{centimeters}=\frac {3}{0.4}=\frac {x}{18} → {x=135}\ {miles}}$$
$${\frac {miles}{inches}=\frac {10}{0.15}=\frac {x}{3} → {x=200}\ {miles}}$$