https://file.aiquickdraw.com/mathbot/file/1726023975520im4860g7.jpg

The question from the image reads:

"A sum of ₹3000 is to be given in the form of 63 prizes. If a prize is of either ₹100 or ₹25, find the number of prizes of each type."

Let's solve this step by step:

Let:
- \( x \) be the number of ₹100 prizes.
- \( y \) be the number of ₹25 prizes.

### Step 1: Form two equations based on the given information.

1. **Total number of prizes**:  
   \( x + y = 63 \)

2. **Total amount of money**:  
   \( 100x + 25y = 3000 \)

### Step 2: Solve the system of equations.

From the first equation, we have:
\[
x + y = 63 \implies y = 63 - x
\]

Substitute \( y = 63 - x \) into the second equation:
\[
100x + 25(63 - x) = 3000
\]

Simplify and solve for \( x \):
\[
100x + 25 \times 63 - 25x = 3000
\]
\[
100x - 25x + 1575 = 3000
\]
\[
75x + 1575 = 3000
\]
\[
75x = 3000 - 1575
\]
\[
75x = 1425
\]
\[
x = \frac{1425}{75} = 19
\]

### Step 3: Find \( y \):
\[
y = 63 - x = 63 - 19 = 44
\]

### Final Answer:
- The number of ₹100 prizes is **19**.
- The number of ₹25 prizes is **44**.

Let me know if you would like further details or explanations!

Here are five related questions:
1. What is a system of linear equations, and how do you solve it?
2. Can you graphically represent the solution to this problem?
3. What happens if the prize amounts change?
4. How would the equation change if there were only 60 prizes?
5. How can the solution be verified using substitution?

**Tip:** Always double-check your solution by substituting the values back into the original equations!

A sum of ₹3000 is to be given in the form of 63 prizes. If a prize is of either ₹100 or ₹25, find the number of prizes of each type.

Learn how to solve the problem of distributing ₹3000 into 63 prizes, where the prizes are either ₹100 or ₹25. This solution uses algebraic methods to solve a system of linear equations. Suitable for students in Grades 8-10.

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