Question

1. a model house is 12 cm wide. if it was built with a scale of 3 cm : 4 m then how wide is the real house? 7) a map has a scale of 2 in : 6 mi. if clayton and centerville are 10 in apart on the map then how far apart are the real cities?

Explanation:

Step1: Set up proportion for model - house problem

Let $x$ be the width of the real - house. The proportion is $\frac{3}{4}=\frac{12}{x}$.

Step2: Cross - multiply

$3x = 4\times12$.

Step3: Solve for $x$

$3x=48$, so $x = 16$ m.

Step4: Set up proportion for map problem

Let $y$ be the distance between the real cities. The proportion is $\frac{2}{6}=\frac{10}{y}$.

Step5: Cross - multiply

$2y=6\times10$.

Step6: Solve for $y$

$2y = 60$, so $y = 30$ mi.

Answer:

The real - house is 16 m wide. The real cities are 30 mi apart.