Scaling a recipe
- Input
- A=4, B=12, C=7
- Expected output
- X = 21
4 cups yield 12 cookies; 7 cups yield 21, keeping the same ratio of 1 cup to 3 cookies.
Carregando ferramenta… / Loading tool…
direct rule of three
In a direct proportion, two quantities grow together at the same rate: A/B = C/X, so X = B×C/A. It works for any pair of quantities linked by a fixed rate, from scaling a recipe to converting a map measurement into a real distance.
4 cups yield 12 cookies; 7 cups yield 21, keeping the same ratio of 1 cup to 3 cookies.
170,000 cm equal 1.7 km; the proportion solves the scale, but converting cm to km still needs a separate step.
With no fixed fee involved, typing more pages takes proportionally more time, with no initial discount or bonus.
In a direct proportion, two quantities grow or shrink together: doubling one doubles the other. You set up A/B = C/X and isolate the unknown with X = B × C / A. For example, if 3 workers produce 6 items per day, 5 workers produce X = 6 × 5 / 3 = 10 items, because more labor yields more output in the same proportion.
Only when the relationship is genuinely proportional, passing through the origin: zero of one quantity must correspond to zero of the other. A taxi ride with a fixed flag-drop fee plus a per-km rate is not a direct proportion, because doubling the distance does not double the total fare, since the flag-drop fee is charged only once.
Just swap B and C in the setup: instead of multiplying the map measurement by 50,000, divide the real distance (already in cm) by 50,000. A real distance of 1700 m (170,000 cm) divided by 50,000 returns exactly the 3.4 cm that would appear on the map.
Yes, within each quantity. In the map example, A and C need to be in centimeters to match the 1:50,000 scale; the result also comes out in centimeters, and converting to meters or kilometers is a manual step done after the calculation.
All calculations stay in your browser. No data is sent to any server.