a lady has only 20 paisa coins and 25 paisa coins in her purse if she has 50 coins in totalling
rupees 11.50 how many coins of each kind does she have
number of 20 paisa coins --- x
number of 25 paisa coins --- 50-x
20x + 25(50-x) = 1150
20x + 1250 - 25x = 1150
-5x = -100
x = 20
so she has 20 of the 20paisa and 30 of the 25 paisa coins
check:
20+30 = 50 , check!
20(20) + 25(30) = 1150 , check!
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To find out how many coins of each kind the lady has, we can use a system of equations.
Let's assume she has 'x' coins of 20 paisa and 'y' coins of 25 paisa. We can represent the total value of coins in terms of paisa as follows:
Total value of 20 paisa coins = 20x paisa
Total value of 25 paisa coins = 25y paisa
According to the given information, the total number of coins is 50, so:
x + y = 50 --------------(Equation 1)
The total value of the coins is given as 11.50 rupees, which is equivalent to 1150 paisa:
20x + 25y = 1150 --------------(Equation 2)
Now, we have a system of two equations with two variables. We can solve these equations simultaneously to find the values of 'x' and 'y'.
To solve the equations, we can use substitution or elimination method. Let's use the elimination method:
Multiply Equation 1 by 20:
20x + 20y = 1000 --------------(Equation 3)
Next, subtract Equation 3 from Equation 2:
20x + 25y - (20x + 20y) = 1150 - 1000
5y = 150
y = 30
Substitute the value of y = 30 into Equation 1:
x + 30 = 50
x = 50 - 30
x = 20
Therefore, the lady has 20 coins of 20 paisa and 30 coins of 25 paisa in her purse.