Capstone: exact recipe scaling

The problem

A baker has a formula written for one batch, but today needs three halves of a batch. Flour is known exactly; water has a small acceptable range. The goal is to scale both quantities without rounding either one.

Before starting, read Expressions, the common inputs in Number notation, and Intervals. The first version needs only named values, multiplication and an interval; no map or tuple is required.

Build the solution

Runnable RiXRun cell

batches := 3 / 2; flourPerBatch := 9 / 4; waterPerBatch := 1:9/8; flour := batches * flourPerBatch; water := batches * waterPerBatch; [flour, water];

How the pieces fit

The first three names are inputs. The next two are derived values. Flour stays a single exact rational; water stays an interval. The final array shows both answers without pretending they have the same kind of certainty. The bounds are exact even though the water amount is uncertain.

Audit the calculation

Start with flour: three halves of nine quarters is twenty-seven eighths. RatCalc may print a mixed form rather than a rounded decimal. Water follows a different path: multiplying its exact bounds by a positive batch count produces the interval 3/2:27/16.

Change batches to 2 and predict both results before rerunning. To inspect the parts separately, replace the last line with flour; or water; and run the cell again.

The key modeling choice is visible: a single fraction represents known flour, while a colon interval preserves the water range.

Extend the model

Add exact sugar at 1/4 per batch. Keep the calculation as a named intermediate so each quantity can be inspected. After Maps, you can report named quantities in a map instead of an array.

Review questions

• What are the scaled flour and water values at three halves of a batch?
• Why is the water result still an interval?
• Which output changes if only the water range changes?