Reena has three times as many 2 rupees coin as he has 5 rupee coins, if she has in all sum of 77 rupees how many coins of each denomination does she have ?

Question

Answer

Answer

**Given information:**
- Reena has three times as many 2 rupees coin as she has 5 rupee coins.
- The sum of all coins is 77 rupees.

To find the number of coins of each denomination, we can follow these steps:

**Step 1: Identify the variables**
Let's assume the number of 5 rupee coins as 'x' and the number of 2 rupee coins as 'y'.

**Step 2: Set up the equations**
Based on the given information, we can set up the following equations:
1. The value of 5 rupee coins (in rupees) = 5x
2. The value of 2 rupee coins (in rupees) = 2y
3. Reena has three times as many 2 rupee coins as 5 rupee coins: y = 3x
4. The sum of all coins is 77 rupees: 5x + 2y = 77

**Step 3: Solve the equations**
We can solve the equations simultaneously to find the values of 'x' and 'y'.

From equation 3, we can substitute the value of 'y' in equation 4:
5x + 2(3x) = 77
5x + 6x = 77
11x = 77
x = 7

Substituting the value of 'x' back into equation 3:
y = 3(7)
y = 21

**Step 4: Interpret the solution**
According to the calculations, Reena has 7 coins of 5 rupees and 21 coins of 2 rupees.

Therefore, Reena has:
- 7 coins of 5 rupees
- 21 coins of 2 rupees

**Final Answer:**
Reena has 7 coins of 5 rupees and 21 coins of 2 rupees.

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