I have 12 coins equalling to 51 cents. What are my coins?

Question

This is one of the math questions that my 8 year old was given for homework. I've tried to help him. I've been on math site after math site - with no luck. Who gives a 3rd grader this kind of question?! I just don't remember math problems being this difficult when I was his age. Can anyone help us?

Answer 1

3 dimes
3 nickels
6 pennies

Answer 2

6pennies
3 nickles
3 dimes

It's really a simple question.

You know you're going to have at least 1 penny, right?

Now you're shooting for 11 coins equaling $.50.

If all are nickles, you'll have $.55, so you know you need more pennies.

Since you can only go in increments of $.05, you'll now have 6 pennies.

Meaning that you'll need to come up with $.45 with 6 coins.

All nickles is too little.
Alll dimes is too much.
1 quarter and all nickles is too much.
Even with a quarter, if you put in another 5 pennies, you'd have too little.

So the answer is some comdination of dimes and nickles.

6 nickels is only $.30.
If you convert a nikel to a dime, you'll add $.05 to the total.
5 nickels and 1 dime is .35
4 nickels and 2 dimes is .40
3 nickels and 3 dimes is .45 !!!!!

Eliminate what possiblities you can and you'll make it easier on yourself.

Answer 3

I am not totally familiar with the US coin system but I assume that you have 1 cent, 5 cents (nickels) and 10 cents (dimes).

All you have is that a + 5b + 10c = 51 and a + b + c = 12

where a b and c are the number of cents, nickels and dimes.

One of the important principles of such equations is that you need 3 equations to solve when three variables are involved. We have only two equations in the above case. So, the problem has no unique solution.

You can physically try out a few combinations of cents, nickels and dimes.

Answer 4

3 dimes 3 nickels and 6 pennies

Answer 5

3 nickles 3 dimes 6cent

Answer 6

3 dimes
3 nickels
6 pennies