Problem
Find the unit amount
A car's distance for a known amount of petrol is given, along with the price per liter. We need what the petrol costs for a longer trip.
RatiosNumber system
Your answer
How to solve
Strategy Analyze the Units — Distance and money are not directly linked -- petrol sits between them. So the chain runs distance, then liters, then won, and the middle link is the distance one liter carries.
1STEP 1
Find the distance on one liter
Divide the distance by the fuel it took.
28.14 ÷ 2.1 = 13.4
One liter carries the car 13.4 km.
6.RP.A.2Analyze The UnitsOne litre carries the car .
Why?
The car covers the same distance on every litre, so the whole distance is a count of equal one-litre stretches.
🧱Multiplication as equal groupsa times b means a equal groups of b — it is just repeated adding of the same amount.
Why?
Finding one such stretch from of them is the division that undoes that count.
🧱Inverse operationsSubtraction undoes addition and division undoes multiplication — they reverse each other.
2STEP 2
Find the fuel the trip needs
Divide the trip's distance by what one liter carries.
335 ÷ 13.4 = 25
The trip takes 25 L.
6.RP.A.3Work Backwards3STEP 3
Work out the cost
Multiply the litres by the price of one litre.
1430 × 25 = 35750
The petrol costs 35,750 won.
6.RP.A.3Identify SubproblemsAnswer
35,750 won
Check the fuel: 13.4 × 25 = 335 km, exactly the trip, and 25 L at 1430 won is 35,750 won.
Takeaway
When two quantities are not directly linked, find the one in the middle and go through it.
- Find the distance on one liter
- Find the fuel the trip needs
- Work out the cost