https://file.aiquickdraw.com/mathbot/file/1726683037499p6m3mgv5.jpg

Let's break down and solve the three parts of this math problem:

### a) Compare the initial sum with 210 lei
First, let's calculate Alisia's initial amount of money based on the given denominations:
- 1 banknote of 100 lei
- 2 banknotes of 50 lei
- 1 banknote of 20 lei
- 3 banknotes of 10 lei
- 4 coins of 1 lei

Calculating this total:
\[
\text{Initial sum} = 100 + (2 \times 50) + 20 + (3 \times 10) + (4 \times 1) = 100 + 100 + 20 + 30 + 4 = 254 \, \text{lei}
\]

The problem asks to compare 254 lei with 210 lei. The true statement is:  
\[
254 > 210
\]

### b) Calculate how much Alisia spent
It is given that after her purchase, Alisia had 12% of her initial sum left. We know the initial sum is 254 lei. The remaining amount is:
\[
\text{Remaining amount} = 12\% \times 254 = 0.12 \times 254 = 30.48 \, \text{lei}
\]

To find out how much she spent:
\[
\text{Amount spent} = 254 - 30.48 = 223.52 \, \text{lei}
\]

### c) Calculate how much Alisia should spend to have 20% of the initial sum left
We are asked to find how much she should spend so that 20% of her initial sum remains. First, calculate 20% of 254 lei:
\[
\text{Remaining amount for 20\%} = 20\% \times 254 = 0.2 \times 254 = 50.8 \, \text{lei}
\]

To find how much she should spend:
\[
\text{Amount to spend} = 254 - 50.8 = 203.2 \, \text{lei}
\]

---

Would you like more details on any step or additional clarification? Here are five related questions to deepen understanding:

1. How would the calculations change if Alisia had 10% of her initial sum left instead of 12%?
2. What would happen if the initial sum was reduced by 15 lei before making any purchases?
3. How can we express the percentage of money spent by Alisia in part b)?
4. How would you calculate the amount left if Alisia spent a different portion of her initial money, say 35%?
5. What is the difference between finding the remaining percentage and calculating the spent percentage in terms of formulas?

**Tip:** When working with percentages, always make sure to convert the percentage into its decimal form (e.g., 12% = 0.12) before performing calculations.

Alisia has a 100 lei banknote, two 50 lei banknotes, a 20 lei banknote, three 10 lei banknotes, and four 1 lei coins. After making a purchase, she is left with 12% of her initial amount. a) Write '>' or '<' in the box to make the statement correct: Initial sum ___ 210 lei. b) Calculate how much Alisia spent. c) Find out how much she needs to spend so that she is left with 20% of her initial amount.

Solve a problem where Alisia starts with an initial sum of money and spends an amount, leaving her with 12%. Calculate the remaining amount and how much she should spend to be left with 20%. Suitable for Grades 5-7.

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