Answer:
Let's denote the number of Rs.1 coins as \( x \), Rs.2 coins as \( y \), and Rs.5 coins as \( z \).
Given:
1. \( x = 2y \) (Number of Rs.1 coins is double the number of Rs.2 coins)
2. \( x + y + z = 100 \) (Total number of coins)
3. \( x + 2y + 5z = 335 \) (Total amount)
Now, we can solve these equations simultaneously:
From equation 1, we get \( x = 2y \).
Substituting this into equations 2 and 3, we get:
\( 2y + y + z = 100 \) and \( 2y + 2y + 5z = 335 \).
Simplifying these equations:
1. \( 3y + z = 100 \)
2. \( 4y + 5z = 335 \)
Now, we have a system of two equations:
1. \( 3y + z = 100 \)
2. \( 4y + 5z = 335 \)
From here, you can solve for \( y \) and \( z \) using any method of solving simultaneous equations. Let me know if you need further assistance!
Answer:
To solve this problem, let's define the number of coins for each denomination:
Let:
- \( x \) = Number of Rs. 1 coins
- \( y \) = Number of Rs. 2 coins
- \( z \) = Number of Rs. 5 coins
We know the following information:
1. The total number of coins is 100:
\[ x + y + z = 100 \]
2. The number of Rs. 1 coins is double the number of Rs. 2 coins:
\[ x = 2y \]
3. The total amount of money from these coins is Rs. 335:
\[ 1x + 2y + 5z = 335 \]
Now substitute \( x = 2y \) into the total number of coins equation:
\[ 2y + y + z = 100 \]
\[ 3y + z = 100 \]
Now substitute \( x = 2y \) and \( z = 100 - 3y \) into the total amount equation:
\[ 1(2y) + 2y + 5(100 - 3y) = 335 \]
\[ 2y + 2y + 500 - 15y = 335 \]
\[ -11y + 500 = 335 \]
\[ -11y = 335 - 500 \]
\[ -11y = -165 \]
\[ y = \frac{-165}{-11} \]
\[ y = 15 \]
Now substitute \( y = 15 \) back into \( x = 2y \) to find \( x \):
\[ x = 2(15) \]
\[ x = 30 \]
Now substitute \( y = 15 \) back into \( z = 100 - 3y \) to find \( z \):
\[ z = 100 - 3(15) \]
\[ z = 100 - 45 \]
\[ z = 55 \]
Therefore, the number of coins of each denomination is:
- Number of Rs. 1 coins (\( x \)) = 30
- Number of Rs. 2 coins (\( y \)) = 15
- Number of Rs. 5 coins (\( z \)) = 55
Verify:
- Total number of coins: \( x + y + z = 30 + 15 + 55 = 100 \)
- Total amount: \( 1x + 2y + 5z = 1(30) + 2(15) + 5(55) = 30 + 30 + 275 = 335 \)
