A payment of ₹120 is made with ₹10, ₹5 and ₹2 coins. A total of 25 coins are used. Which of the following is the number of ₹10 coins used in the payment?

Let's define the number of coins used:

- Let \( x \) be the number of ₹10 coins.
- Let \( y \) be the number of ₹5 coins.
- Let \( z \) be the number of ₹2 coins.

We are given two pieces of information:

1. The total value of the coins is ₹120:
   \[
   10x + 5y + 2z = 120
   \]
2. The total number of coins is 25:
   \[
   x + y + z = 25
   \]

We now have two equations:
1. \( 10x + 5y + 2z = 120 \)
2. \( x + y + z = 25 \)

### Step 1: Solve one equation for one variable
Let's solve equation (2) for \( z \):
\[
z = 25 - x - y
\]

### Step 2: Substitute into the first equation
Substitute \( z = 25 - x - y \) into equation (1):
\[
10x + 5y + 2(25 - x - y) = 120
\]

### Step 3: Simplify the equation
\[
10x + 5y + 50 - 2x - 2y = 120
\]
\[
(10x - 2x) + (5y - 2y) + 50 = 120
\]
\[
8x + 3y + 50 = 120
\]
\[
8x + 3y = 70
\]

### Step 4: Solve for integer values of \( x \) and \( y \)
Now, we need to solve the equation \( 8x + 3y = 70 \).

First, let's try different integer values for \( x \):

- If \( x = 8 \):
  \[
  8(8) + 3y = 70 \implies 64 + 3y = 70 \implies 3y = 6 \implies y = 2
  \]
  Substituting \( x = 8 \) and \( y = 2 \) into \( z = 25 - x - y \):
  \[
  z = 25 - 8 - 2 = 15
  \]

So, the solution is \( x = 8 \), \( y = 2 \), and \( z = 15 \).

### Conclusion:
The number of ₹10 coins used in the payment is **8**.

Would you like further details or have any questions?

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Here are 5 related questions for practice:
1. What if the total payment was ₹150 instead of ₹120?
2. How many coins would be used if only ₹10 and ₹5 coins were available?
3. What if you had an additional coin denomination, say ₹1, in the problem?
4. What is the least number of coins needed to make a payment of ₹120 with ₹10 and ₹5 coins only?
5. How would the solution change if the total number of coins was 30?

**Tip:** When solving systems of equations with integer solutions, substituting values and simplifying can often lead to quicker results.

A payment of ₹120 is made with ₹10, ₹5, and ₹2 coins. A total of 25 coins are used. Which of the following is the number of ₹10 coins used in the payment?

Discover how to solve a coin payment problem where ₹120 is made using ₹10, ₹5, and ₹2 coins, with 25 total coins. Learn key algebraic methods and the substitution approach to find the number of ₹10 coins used. Suitable for Grades 8-10.

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