Let’s solve each problem step by step. The key idea is to
use the given scale factor to set up a proportion and solve for the missing dimension. We’ll convert units when necessary and round to the nearest tenth as instructed.
---
Problem 1:
> The scale factor for a model is
5 cm = ___ m
> Model: 9.5 cm
> Actual: 30.5 m
We need to find how many meters correspond to 5 cm in the model.
Set up a proportion:
\[
\frac{5 \text{ cm}}{x \text{ m}} = \frac{9.5 \text{ cm}}{30.5 \text{ m}}
\]
Cross-multiply:
\[
5 \cdot 30.5 = 9.5 \cdot x
\]
\[
152.5 = 9.5x
\]
\[
x = \frac{152.5}{9.5} ≈ 16.0526...
\]
✔ Answer: 16.1 m
---
Problem 2:
> The scale of a map is
2 m = 4 mi
> Map: 12 m
> Actual: ___ mi
Set up proportion:
\[
\frac{2 \text{ m}}{4 \text{ mi}} = \frac{12 \text{ m}}{x \text{ mi}}
\]
Cross-multiply:
\[
2x = 48
\]
\[
x = 24
\]
✔ Answer: 24.0 mi
---
Problem 3:
> The scale of a map is
2 ft = 10.4 mi
> Map: ___ ft
> Actual: 20.8 mi
Proportion:
\[
\frac{2 \text{ ft}}{10.4 \text{ mi}} = \frac{x \text{ ft}}{20.8 \text{ mi}}
\]
Cross-multiply:
\[
2 \cdot 20.8 = 10.4x
\]
\[
41.6 = 10.4x
\]
\[
x = \frac{41.6}{10.4} = 4
\]
✔ Answer: 4.0 ft
---
Problem 4:
> The scale factor for a model is
7 cm = ___ m
> Model: 40.4 cm
> Actual: 80.6 m
Proportion:
\[
\frac{7 \text{ cm}}{x \text{ m}} = \frac{40.4 \text{ cm}}{80.6 \text{ m}}
\]
Cross-multiply:
\[
7 \cdot 80.6 = 40.4x
\]
\[
564.2 = 40.4x
\]
\[
x = \frac{564.2}{40.4} ≈ 13.965...
\]
✔ Answer: 14.0 m
---
Problem 5:
> The scale of a map is
5 m = 15 mi
> Map: 7.8 m
> Actual: ___ mi
Proportion:
\[
\frac{5 \text{ m}}{15 \text{ mi}} = \frac{7.8 \text{ m}}{x \text{ mi}}
\]
Cross-multiply:
\[
5x = 15 \cdot 7.8 = 117
\]
\[
x = \frac{117}{5} = 23.4
\]
✔ Answer: 23.4 mi
---
Problem 6:
> The scale of a map is
6 km = 4 mi
> Map: ___ km
> Actual: 40.1 mi
Proportion:
\[
\frac{6 \text{ km}}{4 \text{ mi}} = \frac{x \text{ km}}{40.1 \text{ mi}}
\]
Cross-multiply:
\[
4x = 6 \cdot 40.1 = 240.6
\]
\[
x = \frac{240.6}{4} = 60.15
\]
✔ Answer: 60.2 km
---
Problem 7:
> The scale factor for a model is
5 cm = ___ m
> Model: 40.2 cm
> Actual: 60.2 m
Proportion:
\[
\frac{5 \text{ cm}}{x \text{ m}} = \frac{40.2 \text{ cm}}{60.2 \text{ m}}
\]
Cross-multiply:
\[
5 \cdot 60.2 = 40.2x
\]
\[
301 = 40.2x
\]
\[
x = \frac{301}{40.2} ≈ 7.4875...
\]
✔ Answer: 7.5 m
---
Problem 8:
> The scale of a map is
4 m = 18 mi
> Map: 6.8 m
> Actual: ___ mi
Proportion:
\[
\frac{4 \text{ m}}{18 \text{ mi}} = \frac{6.8 \text{ m}}{x \text{ mi}}
\]
Cross-multiply:
\[
4x = 18 \cdot 6.8 = 122.4
\]
\[
x = \frac{122.4}{4} = 30.6
\]
✔ Answer: 30.6 mi
---
Problem 9:
> The scale of a map is
4 ft = 16 mi
> Map: ___ ft
> Actual: 80 mi
Proportion:
\[
\frac{4 \text{ ft}}{16 \text{ mi}} = \frac{x \text{ ft}}{80 \text{ mi}}
\]
Cross-multiply:
\[
16x = 4 \cdot 80 = 320
\]
\[
x = \frac{320}{16} = 20
\]
✔ Answer: 20.0 ft
---
Problem 10:
> The scale factor for a model is
8 cm = ___ m
> Model: 80.8 cm
> Actual: 90.6 m
Proportion:
\[
\frac{8 \text{ cm}}{x \text{ m}} = \frac{80.8 \text{ cm}}{90.6 \text{ m}}
\]
Cross-multiply:
\[
8 \cdot 90.6 = 80.8x
\]
\[
724.8 = 80.8x
\]
\[
x = \frac{724.8}{80.8} ≈ 8.9703...
\]
✔ Answer: 9.0 m
---
##
✔ Final Answers (Rounded to Nearest Tenth):
1.
16.1 m
2.
24.0 mi
3.
4.0 ft
4.
14.0 m
5.
23.4 mi
6.
60.2 km
7.
7.5 m
8.
30.6 mi
9.
20.0 ft
10.
9.0 m
---
Let me know if you’d like to see the work shown differently or need help understanding any step!
Parent Tip: Review the logic above to help your child master the concept of scale drawing worksheet 7th grade pdf.
