Verified answer

Answer:

• The number of 25 paise coins = 30

• The number of 50 paise coins = 70

Step-by-step explanation:

Given :

• There are some 25 paise coins and some  50 paise coins in a bag.
• The total number of  coins = 100.
• The amount in the bag is  Rs 42.50

To find :

the number of 25 paise coins and 50 paise coins

Solution :

Let x be the number of 25 paise coins and y be the number of 50 paise coins.

The total number of coins is 100.

x + y = 100 ➙ [1]

The total amount is Rs 42.50

Convert Rs to paise,

1 rupee = 100 paise

Rs 42.50 = 42.50 × 100 paise = 4250 paise

Now,

 x(25 paise) + y(50 paise) = 4250 paise

  25x + 50y = 4250

  25(x + 2y) = 25(170)

   x + 2y = 170 ➙ [2]

Subtract equation [1] from [2]

x + 2y - (x + y) = 170 - 100

x + 2y - x - y = 70

    y = 70

★ Value of x :

x + y = 100

x + 70 = 100

x = 100 - 70

x = 30

Therefore,

The number of 25 paise coins = 30

The number of 50 paise coins = 70