Question

Toby created a scale drawing of the school cafeteria. In the scale drawing, the length of the cafeteria is 14 inches. The length of the actual cafeteria is 112 feet.


Which scale did Toby use to create the scale drawing of the school cafeteria?

Answer 1

To find the scale used by Toby for the scale drawing, we need to compare the lengths in the drawing to the actual lengths.

1. **Convert the actual length from feet to inches**, since the length in the drawing is in inches. There are 12 inches in a foot, so:
\[
112 \text{ feet} \times 12 \text{ inches/foot} = 1344 \text{ inches}
\]

2. **Now, determine the scale** of the drawing by comparing the length of the drawing to the actual length:
\[
\text{Scale} = \frac{\text{Length of the drawing}}{\text{Actual length}} = \frac{14 \text{ inches}}{1344 \text{ inches}}
\]

3. **Simplifying the fraction**:
\[
\text{Scale} = \frac{14}{1344}
\]
To simplify, divide both the numerator and the denominator by 14:
\[
\frac{14 \div 14}{1344 \div 14} = \frac{1}{96}
\]

So, the scale Toby used for the scale drawing of the school cafeteria is **1 inch : 96 inches**, or equivalently, **1 inch : 8 feet**.