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 26 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 42.9 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 Q9

Let $x$ = width of model. Proportion: $\frac{1}{2} = \frac{x}{26}$

Step2: Solve for Q9 $x$

$x = \frac{26}{2} = 13.0$

Step3: Set up proportion for Q10

Let $h$ = elephant height. Proportion: $\frac{6.5}{33.2} = \frac{h}{51.5}$

Step4: Solve for Q10 $h$

$h = \frac{6.5 \times 51.5}{33.2} \approx 10.1$

Step5: Set up proportion for Q11

Let $s$ = woman's shadow. Proportion: $\frac{42.9}{253.1} = \frac{6.2}{s}$

Step6: Solve for Q11 $s$

$s = \frac{6.2 \times 253.1}{42.9} \approx 36.7$

Step7: Set up proportion for Q12

Let $d$ = real distance. Proportion: $\frac{1.1}{15} = \frac{9.7}{d}$

Step8: Solve for Q12 $d$

$d = \frac{9.7 \times 15}{1.1} \approx 132.3$

Answer:

1. 13.0 in
2. 10.1 ft
3. 36.7 ft
4. 132.3 mi