# A model car was built on a scale of 1:30. If the height of the model car was 1 inches what was the height of the actual car in feet?

Apr 28, 2017

See the entire solution process below:

#### Explanation:

We can write this problem as:

$1 : 30 \to 1 i n : x i n$

Therefore x in = 30 in.

Because 1 ft = 12 in we can write 30 inches as:

$30 i n \cdot \frac{1 f t}{12 i n} = 30 \textcolor{red}{\cancel{\textcolor{b l a c k}{i n}}} \cdot \frac{1 f t}{12 \textcolor{red}{\cancel{\textcolor{b l a c k}{i n}}}} = \frac{30 f t}{12} = 2.5 f t$

The actual height of the car was 2.5 feet.

Apr 28, 2017

$2 \frac{1}{2}$ feet

#### Explanation:

Scale is ratio.

$\implies \text{model : actual } \to 1 : 30$

Write in fraction format:

$\left(\text{model")/("actual}\right) \to \frac{1}{30}$

Actually, in this case, I prefer it up the other way:

$\left(\text{actual")/("model}\right) \to \frac{30}{1}$

But we are told that the model car is 1 inch high so we write:

$\left(\text{actual")/("model")->(30" inches")/(1" inch}\right)$

So the actual car had the height of 30 inches.

(Oh come on! That is silly! I have never seen a car 30" high!)

The question instructs that the height is to be in feet.

1 foot is the same length as 12 inches. So we need to see how many lots of 12 inches we can fit into 30 inches

Actual height in feet is $30 \div 12 = 2 \frac{6}{12}$ feet $\to 2 \frac{1}{2}$feet