Question: Miguel’s savings taken from a piggy bank containing ₱10-coins and ₱20-coins.
Model this using algebraic expressions
Please show me the solution and the model
1. **State the problem:**
We want to model Miguel's savings taken from a piggy bank containing two types of coins: ₱10-coins and ₱20-coins.
2. **Define variables:**
Let $x$ be the number of ₱10-coins.
Let $y$ be the number of ₱20-coins.
3. **Form the algebraic expression for total savings:**
The total amount of money $S$ can be expressed as:
$$S = 10x + 20y$$
4. **Explanation:**
Each ₱10-coin contributes $10$ units to the total savings, and each ₱20-coin contributes $20$ units.
Multiplying the number of each coin by its value and adding gives the total savings.
5. **Additional notes:**
- $x$ and $y$ must be non-negative integers since they represent counts of coins.
- This model can be used to find total savings if $x$ and $y$ are known, or to solve for $x$ or $y$ given total savings and one variable.
**Final model:**
$$S = 10x + 20y$$
This is the algebraic expression modeling Miguel's savings from the piggy bank.