### 18 Answers

- roderick_youngLv 74 months ago
What is more interesting about this problem is to find all solutions.

Assuming this is current US coinage, that is, no 2-cent or 3-cent pieces, 20 cent pieces, etc. Just pennies dimes, nickels, quarters, half dollars, dollars.

There can't be any dollars, as even one would make the total too much.

Now I will consider the pennies. There must be at least one, to make 61 cents. If there are more than one penny, then there must be multiples of 5 pennies added, in order to get a total ending in 1. So there could be 6. But there can't be 11 or more, because there can only be 8 coins total. So there are either 1 or 6 pennies.

Let's look at 6 pennies first. That leaves 55 cents, to make with 2 coins. Only way to do that is a half dollar and a nickel. If a quarter or dime is involved, we cannot get 55 cents with 2 coins.

So

50 + 5 + 1 + 1 + 1 + 1 + 1 + 1 is one solution.

Now how about the case of one penny? That leaves 60 cents to make with 7 coins. If one coin is a half dollar, then we have to make 10 cents with 6 coins. Not possible, so there are no half dollars.

Are there any quarters? If there are two quarters, then we have 10 cents to make with 5 coins, all of which must be dimes or nickels. Not possible (remember, no 2-cent pieces).

How about one quarter? That leaves 35 cents to make with 6 coins, all dimes and nickels. This is an algebra problem with 2 equaltions and 2 variables, so there is only one all-integer solution, if any at all. Happens to be a dime and 5 nickels. So

25 + 10 + 5 + 5 + 5 + 5 + 5 + 1 is another solution.

How about no quarters? That leaves 60 cents to make with only dimes and nickels, 7 coins. Sure, 5 dimes and 2 nickels, and there is no other answer. So

10 + 10 + 10 + 10 + 10 + 5 + 5 + 1 is another solution.

So there are 3 solutions, and no others:

One half dollar, a nickel, and six pennies;

A quarter, a dime, five nickels, and a penny; and

Five dimes, two nickels, and a penny.

- Anonymous4 months ago
5 dimes == 0.50

2 nickels == 0.10

1 penny == 0.01

8 coins === 0.61

Source(s): My brain - What do you think of the answers? You can sign in to give your opinion on the answer.
- geezerLv 74 months ago
OK .. A Nickle is 5 Cents .. a Dime is 10 Cents .. and a Quarter is 25 Cents

So .. That's 1 Cent for the 1

5 Nickles is 25 Cents .. so 1 Quarter and 5 Nickles is 50 Cents

leaving you with 1 Dime for the other 10 Cents .. making it 61 Cents using 8 coins.

1 + 25 + 5 + 5 + 5 + 5 + 5 + 10 = 61 Cents

- PhilLv 64 months ago
25 cents x 1= 25 cents.

10 cents x 1= 10 cents.

5 cents x 5 = 25 cents.

1 cent x 1 = 1 cent.

- DavidLv 74 months ago
50c piece, nickel, and six pennies. There, now what was so difficult about that?