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A scale on a map shows that 2.5 centimeters represents 15 kilometers.
What number of actual kilometers are represented by 17.5 centimeters on the map?

◻ kilometers

A scale on a map shows that $2$ . $5$ centimeters represents $15$ kilometers. $\newline$ What number of actual kilometers are represented by $17$ . $5$ centimeters on the map? $\newline$ $\square$ kilometers

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Scale drawings: word problems

Full solution

Q. A scale on a map shows that

2

.

5

centimeters represents

15

kilometers.

\newline

What number of actual kilometers are represented by

17

.

5

centimeters on the map?

\newline

\square

kilometers

Understand the scale: Understand the scale given on the map. $\newline$ The scale on the map is $2.5$ centimeters represents $15$ kilometers. This means that for every $2.5$ centimeters on the map, the actual distance is $15$ kilometers.
Set up the proportion: Set up the proportion to find the actual distance represented by $17.5$ centimeters. $\newline$ If $2.5$ cm represents $15$ km, then $17.5$ cm represents $x$ km. We can write this as a proportion: $\newline$ $\frac{2.5 \text{ cm}}{15 \text{ km}} = \frac{17.5 \text{ cm}}{x \text{ km}}$
Solve for x: Solve for x, the number of kilometers represented by $17.5$ centimeters. $\newline$ Cross-multiply to solve for x: $\newline$ $2.5 \times x = 15 \times 17.5$ $\newline$ $x = \frac{(15 \times 17.5)}{2.5}$
Perform the calculation: Perform the calculation to find the value of $x$ . $x = \frac{15 \times 17.5}{2.5}$ $x = \frac{262.5}{2.5}$ $x = 105$

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