Scale drawings: word problems
Learn with an example
🔥After a long hike in a national park, Joe decides to go relax at the beach. The parking permit he purchased allows him to park at any state beach without paying again. While consulting a map, Joe notices that the closest state beach is 9 centimetres away from the park. The scale of the map is 1 centimetre = 1 kilometre. In real life, what is the distance between the national park and the closest state beach?
______ kilometres
- Write a ratio that represents the scale of the map in centimetres to kilometres: 1/1,
- Write a ratio that relates the centimetres between the state park and the closest state beach on the map to the kilometres between the state park and the closest state beach in real life: 9/d,
- Use those ratios to set up a proportion and solve.
- 1/1 = 9/d
- 1/1 ( d ) = 9/d ( d ) ——-> Multiply both sides by d
- d = 9 ——-> Simplify
- In real life, the distance between the national park and the closest state beach is 9 kilometres.
🔥Judy is on a road trip and notices that, according to the map, the next petrol station on her route is 7 centimetres away. If the scale of the map is 1 centimetre = 10 kilometres, then what is the actual distance between the two petrol stations?
______ kilometres
- Write a ratio that represents the scale of the map in centimetres to kilometres: 1/10.
- Write a ratio that relates the centimetres between the two petrol stations on the map to the kilometres between the two petrol stations in real life: 7/d.
- Use those ratios to set up a proportion and solve.
- 1/10 = 7/d
- 1/10 ( 10d ) = 7/d ( 10d ) ——-> Multiply both sides by 10d
- d = 10 · 7 ——–> Simplify
- d = 70 ———> Simplify
- The actual distance between the two petrol stations is 70 kilometres.
🔥On a public transportation map, two stations are 6 centimetres apart, whereas in real life the distance between them is 2 kilometres. What is the map’s scale?
Write your answer in the simplest form using whole numbers.
______ centimetres = _______ kilometres
- Write a ratio that relates the centimetres between the two stations on the map to the kilometres between the two stations in real life: 6/2.
- To find the scale of the map, rewrite this ratio in simplest form using whole numbers.
- 6/2 = 3/1 —–> Divide the numerator and denominator by the GCF, which is 2
- The map’s scale is 3 centimetres = 1 kilometre.
Let’s practice! 🖊️