Question

Akshaya has 2 rupee coins and 5 rupee coins in her purse. If in all she has 80 coins totalling ₹ 220, how many coins of each kind does she have.

Answer 1

Let the number of 2 rupee coins be “x” and the number of 5 rupee coins be “y”.

By the given first condition

x + y = 80 → (1)

Again by the given second condition

2x + 5y = 220 → (2)

x + y – 80 = 0 → (3)

2x + 5y – 220 = 0 → (4)

Using the coefficients for cross multiplication

`x/(-220 - (-400)) = y/(-160 - (-220)) = 1/(5 - 2)`

`x/(-220 + 400) = y/(-160 + 220) = 1/3`

`x/180 = y/60 = 1/3`

`x/180 = 1/3`

3x = 180

x = `180/3`

= 60

But `y/60 = 1/3`

3y = 60

y = `6/30`

= 20

Number of 2 rupee coins = 60

Number of 5 rupee coins = 20