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

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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(19441) (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
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20 quarters + 0 pennies = 20 coins
19 quarters + 25 pennies = 45 coins
18 quarters + 50 pennies = 68 coins
17 quarters + 75 pennies = 92 coins
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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
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15 quarters + 5 dimes + 75 pennies = 95 coins
15 quarters + 4 dimes + 85 pennies = 104 coins
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10 quarters + 15 dimes + 100 pennies = 125 coins
10 quarters + 20 dimes + 50 pennies = 80 coins
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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

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