# Building a solution model (algebra)

Consider the following story problem.

Nicole buys a sweater for €63,50. The original price was €74,95.
What percentage was the discount? Round your answer to the nearest whole number.

You can define this exercise with a single task as follows:

However, a student will probably split his solution in parts:

1. Calculate the price difference $€74.95-€63.50$
2. Calculate the difference as a factor: $\frac{difference}{€74.95}$
3. Convert the fraction into a percentage: $factor \times 100%$

You can define such a solution model in AlgebraKiT, so that these intermediate steps are correctly evaluated.

• Create an interaction of type algebra
• Add a step using the green plus + symbol, next to the word ‘solution’. Click on the triangle to name this step ‘factor’.  Add another step and call it ‘difference’.
• Give each step a description. The description defines ‘what’ this step means and is used by AlgebraKiT to generate hints and worked solutions.
Give the steps the descriptions: “the price difference”, “the discount as a decimal number” and “the discount as a percentage”.
• Set the mathematical task for each step.
•  $€74.95-€63.50$
• $\frac{difference}{€74.95}$
• $factor \times 100%$
• Set accuracy. Step ‘factor’ should be accurate to at least 3 decimal places. The solution step must be rounded to 0 decimal places.

Run the exercise to see the result:

Interactive student exercise:

Worked solution:

Students often make the mistake to use the wrong price for calculating the percentage. You can add feedback for such input.

### Multiple solution strategies

A student could also use a difference approach to solve this problem:

1. Calculate the discounted price as a factor
2. Convert this factor into a percentage
3. Calculate the discount percentage

You can add steps 1 and 2 to the solution model in the same way as you did before. Step 3 defines the final answer, which was 15%. By adding an extra task to the step ‘solution’ with the definition based on the newly added steps, AlgebraKiT ‘knows’ there are two ways to calculate the solution.