Mr. Lucido deposited 225 pesos in the bank. If his deposit consisted of 29 bills, consisting of 5 peso and 10 peso bills, how many 10 peso bills did he deposit

Let's define the variables:
- Let \( x \) be the number of 5-peso bills.
- Let \( y \) be the number of 10-peso bills.

From the problem, we have two pieces of information:

1. The total number of bills is 29, so:
   \[
   x + y = 29
   \]
   
2. The total value of the deposit is 225 pesos, so:
   \[
   5x + 10y = 225
   \]

We now have a system of two equations:
1. \( x + y = 29 \)
2. \( 5x + 10y = 225 \)

### Solving the system of equations:

First, simplify the second equation by dividing everything by 5:
\[
x + 2y = 45
\]

Now, subtract the first equation from the simplified second equation:
\[
(x + 2y) - (x + y) = 45 - 29
\]
This simplifies to:
\[
y = 16
\]

So, Mr. Lucido deposited **16 ten-peso bills**.

### Verification:
- If \( y = 16 \), then from \( x + y = 29 \), we get \( x = 29 - 16 = 13 \).
- The value of the deposit is \( 5(13) + 10(16) = 65 + 160 = 225 \), which matches the total amount.

Therefore, Mr. Lucido deposited 16 ten-peso bills.

Do you need further explanation or more details? Here are some related questions to explore:

1. What is the general method for solving systems of linear equations?
2. How can you check if a system of equations has no solution or infinite solutions?
3. How would the problem change if he deposited only 200 pesos with the same number of bills?
4. What other combinations of bills could sum to 225 pesos if other denominations were available?
5. How can you solve this problem using matrices or substitution?

**Tip:** Always verify your solution by plugging the values back into the original equations to ensure consistency.

Mr. Lucido deposited 225 pesos in the bank. If his deposit consisted of 29 bills, consisting of 5 peso and 10 peso bills, how many 10 peso bills did he deposit?

Learn how to solve a system of linear equations using algebra. This problem involves determining the number of 10 peso bills from a total deposit of 225 pesos, using two equations to represent the total number of bills and their value. Suitable for Grades 6-8 students.

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