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I've tried to solve this math problem using real coins,but I can't find the answer!!?

Often, for fun I like to look up math problems on the internet and then try to solve them :) (lol so dorkyyyy).!!!! And this is the problem: Find how many ways you can make $1.62 from pennies, dimes, and nickels if half of the coins used must be nickels. List each possible solution. I've tried using real coins, and I must have worked for over an hour trying to figure it out!!! It's sooo hard. And I really can't figure it out. Does anyone know the answer? Thank you because it will save me so much more frustration :( :) gracias

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1. Let the number of pennies be x, the number of dimes be y. As the number of nickels is half the total number of coins, the number of nickels is equal to the number of pennies plus the number of dimes. So the number of nickles is x + y. x + 5(x + y) + 10y = 162 6x + 15y = 162 2x + 5y = 54 x = (54 - 5y)/2 As x has to be an integer, (54 - 5y) has to be divisible by 2. This will be satisfied only when y is an even integer and 5y < 54, or y <= 10. In short, all the solutions possible can be listed as follows: For any even integer integer n <= 10: y = n x = (54 - 5n)/2 x + y = n + (54 - 5n)/2 = (54 - 3n)/2 This way, you can generate all the possible solutions, there will be 6 in total. For example, when n = 2: y = 2 x = 22 x + y = 24 So, the number of dimes is 2, the number of pennies is 22 and the number of nickels is 24. Check this: 2 * 10 + 22 + 24 * 5 = 20 + 22 + 120 = 162 = $1.62. Hope this helps.
2. There are 5 ways: 1. 22 pennies 24 nickels 2 dimes 2. 17 pennies 21 nickels 4 dimes 3. 12 pennies 18 nickels 6 dimes 4. 7 pennies 15 nickels 8 dimes 5. 2 pennies 12 nickels 10 dimes Let there be p pennies, n nickels and d dimes. Since half of the coins used are nickels, so n = p + d We have 1p + 5n + 10d = 162 or 1p + 5p + 5d + 10d = 162 or 6p + 15d = 162 or p = { 162 - 15d } / 6 or p = 27 - 5d/2 For p to be positive integer d must be even and less than 11. Thus we get 5 values for d {2,4,6,8,10}.
3. Hi, Try these: 5 quarters, 2 pennies, 7 nickels 4 quarters, 2 dimes, 2 pennies, 8 nickels 3 quarters, 4 dimes, 2 pennies, 9 nickels 2 quarters, 6 dimes, 2 pennies, 10 nickels 10 dimes, 2 pennies, 12 nickels I hope that helps!! :-)