Scale Factors word problems online exercise for - Free Printable

Let's solve each problem step by step using scale factors. A scale factor relates the size of a model or drawing to the actual size of the object it represents.

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1) Helen and Mandy's Cities

- Given:
- Distance on map = 3 inches
- Scale factor: 1 mile = 0.016 inch

We need to find the actual distance in miles.

This means:
> 0.016 inch on the map = 1 mile in real life

So, how many miles does 3 inches represent?

Set up a proportion:
$$
\frac{1 \text{ mile}}{0.016 \text{ inch}} = \frac{x \text{ miles}}{3 \text{ inches}}
$$

Solve for $ x $:
$$
x = \frac{3}{0.016} = 187.5 \text{ miles}
$$

✔ Answer: 187.5 miles

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2) Photo Backdrop Enlargement

- Given:
- Actual length of photo = 5 inches (this is the original digital image)
- Scale factor: 1 inch (on print) = 2.2 feet (in reality)

Wait — this is a print enlargement, so we're scaling up from the original digital image.

But the original image is 5 inches, and they are printing it larger using a scale factor of 1 inch (on the print) = 2.2 feet (real).

Wait — let's clarify:

> "The actual length of the photo was 5 inches" → this is likely the original digital image.

They want to enlarge it with a scale factor of 1 inch (model) = 2.2 feet (actual).

But that doesn't make sense unless we interpret it differently.

Actually, here’s the key:

> The digital image is 5 inches long, and the printing company uses a scale factor of 1 inch = 2.2 feet to enlarge the image.

That means:
For every 1 inch in the digital image, the printed version is 2.2 feet long.

So, if the digital image is 5 inches, then:

$$
\text{Printed length} = 5 \times 2.2 = 11 \text{ feet}
$$

✔ Answer: 11 feet

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3) Harry’s Dollhouse

- Given:
- Actual height of home = 17.86 feet
- Scale factor: 1 inch = 3.8 feet

We want the height of the dollhouse (the model), which is smaller.

So, use:
$$
\text{Model height (inches)} = \frac{\text{Actual height}}{\text{Scale factor per inch}} = \frac{17.86}{3.8}
$$

Calculate:
$$
\frac{17.86}{3.8} = 4.7 \text{ inches}
$$

✔ Answer: 4.7 inches

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4) Diane’s Boat Model

- Given:
- Scale factor: 1 foot (actual) = 0.1 inch (model)
→ So, 1 foot in real life = 0.1 inch in model
→ This means: 1 inch in model = 10 feet in real life (since 1 / 0.1 = 10)

- Mast in model = 2.5 inches

So actual height:
$$
2.5 \times 10 = 25 \text{ feet}
$$

✔ Answer: 25 feet

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5) Zebra Model

- Given:
- Model height = 8 inches
- Scale factor: 1 inch = 0.62 foot

So, actual height:
$$
8 \times 0.62 = 4.96 \text{ feet}
$$

✔ Answer: 4.96 feet

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6) Truck Model

- Given:
- Model length = 12 inches
- Scale factor: 1 inch = 4 feet

So, actual length:
$$
12 \times 4 = 48 \text{ feet}
$$

✔ Answer: 48 feet

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✔ Final Answers:

1) 187.5 miles
2) 11 feet
3) 4.7 inches
4) 25 feet
5) 4.96 feet
6) 48 feet

Let me know if you'd like these written neatly for submission!