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A scale on a blue print drawing of a house shows that 6 centimeters represents 3 meters.
What number of centimeters on the blue print represents an actual distance of 27 meters?
centimeters

A scale on a blue print drawing of a house shows that $6$ centimeters represents $3$ meters. $\newline$ What number of centimeters on the blue print represents an actual distance of $27$ meters? $\newline$ centimeters

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Solve proportions: word problems

Full solution

Q. A scale on a blue print drawing of a house shows that

6

centimeters represents

3

meters.

\newline

What number of centimeters on the blue print represents an actual distance of

27

meters?

\newline

centimeters

Establish Scale Ratio: First, we need to establish the scale ratio between the blueprint and the actual size. The scale given is $6$ centimeters on the blueprint represents $3$ meters in actual size.
Determine Centimeters to Meters Ratio: Next, we need to determine the ratio of centimeters to meters according to the scale. This is found by dividing the number of centimeters on the blueprint by the number of meters they represent. $\newline$ Ratio = $\frac{6\,\text{cm}}{3\,\text{m}}$
Convert Ratio to Centimeters per Meter: To make it easier to use, we can convert the ratio into centimeters per meter by dividing both sides of the ratio by $3$ . $\newline$ Ratio = $(6 \, \text{cm} / 3 \, \text{m}) / 3 = 2 \, \text{cm} / 1 \, \text{m}$
Calculate Blueprint Distance: Now, we need to use this ratio to find out how many centimeters on the blueprint represent an actual distance of $27$ meters. We do this by multiplying the actual distance by the ratio. $\newline$ Blueprint distance = Actual distance $*$ Ratio $\newline$ Blueprint distance = $27$ m $*$ $2$ cm/m
Perform Multiplication: Perform the multiplication to find the blueprint distance. $\newline$ Blueprint distance = $27 \times 2\,\text{cm}$ $\newline$ Blueprint distance = $54\,\text{cm}$

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