# SOLUTION: Suppose you want to make \$5 using exactly 100 common US coins. Easy, you say: just use nickels (5 cents each). But I say, no - we have NO nickels, only pennie

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 Question 492814: Suppose you want to make \$5 using exactly 100 common US coins. Easy, you say: just use nickels (5 cents each). But I say, no - we have NO nickels, only pennies (1 cent), dimes (10 cents) and quarters (25 cents) - is it possible to make \$5 now with exactly 100 of these coins? Why or why not?Answer by josmiceli(9669)   (Show Source): You can put this solution on YOUR website!Start with 20 quarters, and only use pennies until you can reach at least 100 coins --------------------------- 20 quarters + 0 pennies = 20 coins 19 quarters + 25 pennies = 45 coins 18 quarters + 50 pennies = 68 coins 17 quarters + 75 pennies = 92 coins ----------------------------- So there must be at THE MOST 16 quarters 16 quarters + 100 pennies = 116 coins 16 quarters + 1 dime + 90 pennies = 107 coins 16 quarters + 2 dimes + 80 pennies = 98 coins ------------------------------ 15 quarters + 5 dimes + 75 pennies = 95 coins 15 quarters + 4 dimes + 85 pennies = 104 coins ------------------------------ 10 quarters + 15 dimes + 100 pennies = 125 coins 10 quarters + 20 dimes + 50 pennies = 80 coins ----------------------------------------- I think this is as close as you will get. The problem is that both the sum of money you need and the number of coins both are multiples of , and that means each of the number of quarters, dimes and pennies all have to be divisible by , and all together, by . So, or quarters is allowed, but neither will give you coins