[wolfgang]

Steve collects coins(but only the small ones!!..1 cent...2cents..and 5 cents).After few weeks he reached(n)number of the three types,where, 73< n < 93.

He noticed that :

The Total value of all coins(in Cents) = Total weight of all coins (in grams)

1- find (n)?

2- find number of 1 cent coins,2 cents,and 5 cents in this mixture(they are different numbers).

knowing that:

1 cent = 2 gm

2 cents = 3 gm

5 cents = 4 gm

[Guest]

Since the number of 1-cent coins plus the number of 2-cent coins must equal the number of 5-cent coins the total number of coins is any even number between 73 and 93.

For example, 1,36,37 for a total of 74 coins yields 258 for value and weight.

[Guest]

Let a = number of 1-cent coins

b = number of 2-cent coins

c = number of 5-cent coins

Then total value = total weight

a + 2b + 5c = 2a + 3b + 4c

5c = a + b + 4c

c = a + b

Thus, the number of 1-cent coins plus the number of 2-cent coins equals the number of 5-cent coins.

Why, does n have to be even?

Edit: Oh wait, I figured it out. Sorry all.

Edited July 7, 2011 by sacohen0326

[superprismatic]

There are 425 possible solutions:

For each number of 5¢ pieces between 37 and 46,

we can have any numbers of 1¢ and 2¢ pieces as

long as they add up to the number of 5¢ pieces.

For example, if the number of 5¢ pieces is 37,

then the number of 1¢ pieces can be any number

from 0 to 37 and the number of 2¢ pieces would

be 37-(# of 1¢ pieces).

[wolfgang]

That was really easy....