Question

1. kayla is making a scale - drawing of a room in a house. the room actually measures 18 feet by 15 feet. using the scale 1 in: 1.5 ft, what are the dimensions of the room in her drawing?
2. star made a scale drawing of her bedroom. in the drawing, the scale is 1/4 inch: 1 foot. if the closet measures 1/2 inch by 3/4 inch, what are the actual dimensions of the closet?
3. an has a map with a scale of 1 inch: 18 miles. to get between two cities on the map, she measures 4.5 inches. how far would that be in real life?

Explanation:

Step1: Recall scale - distance formula

The formula for scale is $\text{Scale}=\frac{\text{Map/Model distance}}{\text{Actual distance}}$. We can re - arrange it to find the actual distance or the map/model distance.

1. For Kayla's room:

The scale is $1$ in : $15$ ft. The actual room is $30$ ft by $45$ ft.
Let the length on the drawing be $l$ and the width be $w$.
For the length:
Since $\frac{1}{15}=\frac{l}{30}$, cross - multiply gives $15l = 30$, so $l=\frac{30}{15}=2$ inches.
For the width:
Since $\frac{1}{15}=\frac{w}{45}$, cross - multiply gives $15w = 45$, so $w=\frac{45}{15}=3$ inches.

2. For Star's closet:

The scale is $\frac{1}{4}$ in : $1$ ft. The closet on the drawing is $\frac{1}{4}$ in by $\frac{1}{2}$ in.
Let the actual length be $L$ and the actual width be $W$.
For the length:
Since $\frac{\frac{1}{4}}{1}=\frac{\frac{1}{4}}{L}$, cross - multiply gives $\frac{1}{4}L=\frac{1}{4}$, so $L = 1$ ft.
For the width:
Since $\frac{\frac{1}{4}}{1}=\frac{\frac{1}{2}}{W}$, cross - multiply gives $\frac{1}{4}W=\frac{1}{2}$, then $W=\frac{1/2}{1/4}=\frac{1}{2}\times4 = 2$ ft.

3. For An's map:

The scale is $1$ in : $18$ miles. The distance on the map is $4.5$ inches.
Let the actual distance be $d$.
Since $\frac{1}{18}=\frac{4.5}{d}$, cross - multiply gives $d=4.5\times18 = 81$ miles.

Answer:

1. The dimensions of Kayla's room in the drawing are 2 inches by 3 inches.
2. The actual dimensions of Star's closet are 1 ft by 2 ft.
3. The actual distance between the two cities is 81 miles.