I have a math question we can't figure out how to get the answer. Please help!!My son is in tears.?

Question

The question is. You have 84 cents, these are all coins. Coins have to weigh 44.5 grams. A dime weighs 2.5 grams, a penny weighs 3.25 grams, a nickle weighs 5.0 grams, a quarter weighs 6.5 grams, and a half dollar weighs 13.0 grams. Please help us, and tell us how you came up with this answer.

Answer 1

First because 2 quarters = 1 half dollar in weight and value get rid of the half dollar to simplify (you can use it to replace 2 quarters later if you want)

Second, to make 84 cents, you need at least 4 pennies, and because of its odd weight, you can see that there needs to be an even number of pennies (if not, the weight would have a value in the .05 range) Knowing that it needs to be even, 5 pennies cannot replace a nickel, but can replace a dime. However if we did that we would have 4 + 10 pennies total and that would weigh too much at 45.5 Grams. So now we know that there are only 4 pennies.

Subtract that from the weight and money and you are down to $0.80 and 31.5 Grams made up of nickels, dimes, and quarters. This is much easier to work with. A quick list of the combinations will give us our answer. 4 pennies, 3 nickels, 4 dimes, 1 quarter.

Answer 2

You must use 4, 9, 14, 19, etc. pennies for the amount to work out.

If you use 14 pennies, they will weigh 45.5 grams, which is too much.

So, you must use either 4 or 9 pennies.

If you use 4 pennies, you have 80 cents left weighing 31.5 grams.

If you use 9 pennies, you have 75 cents left weighing 15.25 grams. Since pennies are the only coin that have a weight measured in quarter grams, you can't have 9 pennies. Therefore, you have exactly 4 pennies.

You have 80 cents remaining to account for, weighing 31.5 grams.

If you use all nickels, they would weigh 80 grams (too much) and if you use all dimes, they would weigh 20 grams (too little).

If you use only nickels and dimes, the equations are 2.5d + 5n = 31.5 and 10d + 5n = 80.

Subtacting the first equation from the second gives 7.5d = 49.5
That would give an amount of dimes that is not a whole number, so there is at least one quarter.

Since a quarter weighs 6.5 grams, that leaves 25 grams and 55 cents.

The two new equations for nickels and dimes are:
10d + 5n = 55
2.5d + 5n = 25
Subtracting the second equation from the first gives
7.5d = 30
So d= 4
Substituting in either equation, gives n = 3

So there are 1 quarter, 4 dimes, 3 nickels and 4 pennies. There are no half dollars.

If the solution had come out with more than one quarter, there would be multiple correct answers since two quarters equal one half dollar in both cents and grams.

Answer 3

OK, you know for sure that you have 4 pennies and their weight is 13.0 grams. Subtract that from the toal weight of 44.5 and you get 31.5 grams. Then you need to go thru waht combinations of coins make 80 cents (what you have left after subtracting the pennies).
I kept doing combinations of coins and their weights until I came up with i quarter (6.5 grams) + 4 dimes (10.0 grams) + 3 nickles (15 grams) . You add all the grams together to get the weight left (31.5) grams.
6.5+10.0+15.0= 31.5 grams
Therefore you have 4 pennies, 1 quarter, 4 dimes and 3 nickles (.04+..25+ 40+.15) = .84

Answer 4

First, you figure out all the different ways to make 84 cents and then calculate the weight of each way. One of the combinations should work unless the teacher didn't check out the answer first.

Answer 5

4 pennies, 3 nickels, 4 dimes, 1 quarter.

Basically used a spreadsheet to make it easy to guess. Look at all the combinations, and let the spreadsheet tell you the value and weight.

Answer 6

1 quarter,4 dimes,3 nickels, and 4 pennies

Answer 7

If this were my son, I would tell him that a math question is nothing to get that worked up over. He can go to school tomorrow, tell his teacher that he couldn't figure it out, and ask for help.