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AQA GCSE · Question 17 · Ratio Proportion and Rates of Change
A map has a scale of 1 : 4000. On the map, the distance from a station to a museum is 7 cm. Is the actual distance from the station to the museum more than 300 m? Show working to support your answer.
A map has a scale of 1 : 4000. On the map, the distance from a station to a museum is 7 cm. Is the actual distance from the station to the museum more than 300 m? Show working to support your answer.
How to approach this question
1. Understand the scale: 1 : 4000 means 1 unit on the map represents 4000 units in reality.
2. The map distance is 7 cm.
3. Calculate the actual distance in cm: 7 cm * 4000 = 28000 cm.
4. Convert the actual distance to metres. There are 100 cm in 1 m, so divide by 100.
5. 28000 cm / 100 = 280 m.
6. Compare this result to 300 m. Is 280 m more than 300 m? No.
7. State your conclusion.
Full Answer
No.
Working:
Actual distance = Map distance × Scale factor
Actual distance = 7 cm × 4000 = 28000 cm.
To convert cm to m, divide by 100.
Actual distance = 28000 / 100 = 280 m.
280 m is not more than 300 m.
Step 1: Calculate the actual distance using the scale.
The scale is 1 : 4000. This means that 1 cm on the map represents 4000 cm in real life.
The distance on the map is 7 cm.
Actual distance in cm = 7 × 4000 = 28 000 cm.
Step 2: Convert the actual distance to metres.
We know that 1 metre = 100 centimetres.
To convert from cm to m, we divide by 100.
Actual distance in m = 28 000 / 100 = 280 m.
Step 3: Compare the actual distance to 300 m.
The question asks if the actual distance is *more than* 300 m.
Our calculated distance is 280 m.
280 m is less than 300 m.
Therefore, the actual distance is not more than 300 m. The answer is No.
Common mistakes
✗ Multiplying by 100 instead of dividing to convert cm to m (or vice versa).
✗ Making a calculation error in the multiplication.
✗ Calculating correctly but making the wrong conclusion (e.g., writing "Yes" after finding 280 m).
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