Question

answer each question and round your answer to the nearest tenth.

1. a model house has a scale of 1 in. : 2 ft. if the real house is 25 ft wide then how wide is the model house?
2. a 6.5 ft tall car standing next to an adult elephant casts a 33.2 ft shadow. if the adult elephant casts a shadow that is 51.5 ft long then how tall is it?
3. if a 4.9 ft tall flagpole casts a 253.1 ft long shadow then how long is the shadow that a 6.2 ft tall woman casts?
4. georgetown and franklin are 9.7 in apart on a map that has a scale of 1.1 in : 15 mi. how far apart are the real cities?

Explanation:

Step1: Set up proportion

For each problem, we set up a proportion based on the given scale or ratio relationship.

Step2: Cross - multiply

Multiply the cross - terms of the proportion to get an equation.

Step3: Solve for the unknown

Isolate the unknown variable in the equation to find the answer.

Answer:

1. Let the width of the model house be $x$ inches. The scale is $1$ in : $2$ ft. The real - house is 25 ft wide. We set up a proportion $\frac{1}{2}=\frac{x}{25}$. Cross - multiplying gives $2x = 25$, so $x=\frac{25}{2}=12.5$ inches.
2. Let the height of the adult elephant be $h$ feet. We set up a proportion using the height - to - shadow ratio. For the car, the ratio of height to shadow is $\frac{6.5}{33.2}$. For the elephant, it is $\frac{h}{51.5}$. So $\frac{6.5}{33.2}=\frac{h}{51.5}$. Cross - multiplying gives $33.2h=6.5\times51.5$, $33.2h = 334.75$, and $h=\frac{334.75}{33.2}\approx10.1$ feet.
3. Let the length of the woman's shadow be $s$ feet. The ratio of the flagpole's height to its shadow is $\frac{42.9}{233.1}$. The ratio of the woman's height to her shadow is $\frac{6.2}{s}$. Setting up a proportion $\frac{42.9}{233.1}=\frac{6.2}{s}$. Cross - multiplying gives $42.9s=6.2\times233.1$, $42.9s = 1445.22$, and $s=\frac{1445.22}{42.9}\approx33.7$ feet.
4. Let the actual distance between the two cities be $d$ miles. The scale is $1.1$ in : $15$ mi. The distance on the map is 9.7 inches. We set up a proportion $\frac{1.1}{15}=\frac{9.7}{d}$. Cross - multiplying gives $1.1d=9.7\times15$, $1.1d = 145.5$, and $d=\frac{145.5}{1.1}\approx132.3$ miles.