a tip jar contains 48 coins, all nickels, dimes, and quarters. the total value of the coins in 5.40. if thr value of the dimes is 55 cents less than the value of the nickels how many of each coin is in the jar?

number of nickle coins = 20

number of dime coins = 11

number of quarter coins = 17

Step-by-step explanation:

Worth of coins in one dollar : 1 quarter = 25%, 1 dime = 10%, 1 nickle = 5%

Now, let number of nickle coins be x and number of quarter coins be y

Number of dimes = 55% less than number of nickle

⇒ Number of dimes = 0.55·x

Now, according to question, Total number of coins in the jar = 48

⇒ x + 0.55·x + y = 48

⇒ 1.55·x + y = 48 ... (1)

Total value of coins in the jar = 5.40

⇒ 0.05·x + 0.01 * 0.55·x + 0.25·y = 5.40

⇒ 0.0555·x + 0.25·y = 5.40

⇒ 5.55·x + 25·y = 540 ... (2)

On solving (1) and (2), We get

x = 19.88 ≈ 20

y = 17.19 ≈ 17

Hence, number of nickle coins = 20

number of dime coins = 11

number of quarter coins = 17