Question

I have a total of 120 in coins of denomination of 1, 2 and 5. The number of 2 coins is double the number of 5 coins. The total number of coins is 60. How many coins of each denomination ate with me? ​

Answer 1

Answer:

• 30 coins of 1 $ ; 20 coins of 2 $ ; 10 coins of 5 $.

Explanation:

Given,

• Total sum I have with me = 120 $
• I have coins of denomination of 1, 2, 5
• Number of 2 $ coins is double the number of 5 $ Coin.
• Total number of coins = 60

To find,

• Number of coins of each denomination I have.

Solution,

Let, I have x, y and z number of coins of denomination 1, 2 and 5 respectively

then,

Since Number of 2 $ coins is double the number of 5 $ coins therefore,

→ y = 2 z  ____equation ①

so,

→ Total number of coins = 60

→ x + y + z = 60

using equation ①

→ x + 2 z + z = 60

→ x + 3 z = 60  

→ x = 60 - 3 z   _____equation ②

and

sum of all 1 $ coins = x (1) = x

sum of all 2 $ coins = y (2) = 2 y

sum of all 5 $ coins = z (5) = z

so,

→ Total sum of money = 120 $

→ x + 2 y + 5 z = 120  

using equation ①

→ x + 2 ( 2 z ) + 5 z = 120

→ x + 4 z + 5 z = 120

→ x + 9 z = 120

using equation ②

→ ( 60 - 3 z ) + 9 z = 120

→ 60 + 6 z = 120

→ 6 z = 60

→ z = 10

putting value of z in equation ②

→ x = 60 - 3 z

→ x = 60 - 3 ( 10 )

→ x = 30

putting value of z in equation ①

→ y = 2 z

→ y = 2 ( 10 )

→ y = 20

Therefore, I have

• 30 coins of 1 $
• 20 coins of 2 $
• and, 10 coins of 5 $ .