denomination does she have?
15. I have a total of 300 in coins of denomination 1,2 and 5. The
number of 2 coins is 3 times the number of 5 coins. The total number of
coins is 160. How many coins of each denomination are with me?
16. The organisers of an essay competition decide that a winner in the
competition gets a prize of 7 100 and a participant who does not win gets
a prize of 25. The total prize money distributed is 3,000. Find the
number of winners, if the total number of participants is 63.
Answers
Answer:
15) there are 60 ₹2 coins, 20 ₹5 coins and 80 ₹1 coins.
16) there are 19 winners.
Step-by-step explanation:
15) let the number of ₹2 coins be x
=> number of ₹5 coins = x/3 and number of ₹1 coins = 160-(x+(x/3)) = 160-(4x/3) (since number of 2 coins is 3 times the number of 5 coins)
ATQ,
total value of coins = 2×x + 5×x/3 + 1×(160-(4x/3))
=> 300 = 2x + 5x/3 + 160 - 4x/3 = 2x + x/3 + 160
=> 2x + x/3 = 140
=> 7x/3 = 140
=> x/3 = 20
=> x = 60
=> x/3 = 20
=> 160-(4x/3) = 80
16) prize for winning = ₹100 (I'm not considering 7100 as you have written because the total money is less than it)
prize for those who didn't win = ₹25
let the number of winners be x
=> the number of non-winners = 63-x
ATQ, 25(63-x) + 100x = 3000 (since the total money is 3000)
=> 1575 - 25x + 7100x = 3000
=> 1425 = 75x
=> x = 19