Question 1117804: Hello and Salutations! I am working on a coin based problem that seems to require making various combinations of the data presented in order to see how many combinations of 4 of any of the coins in the table make up the summed amounts in options given. I can honestly say that it probably would take awhile to come up with all the combinations possible to see which sums can apply for the answers...
Matt has 10 coins, and their values are shown in the table. If he randomly selects 4 coins, which of the following could be the total value of the 4 coins? SELECT ALL THAT APPLY
Table: Coin Value #of Coins
$0.01 3
$0.05 3
$0.10 3
$0.25 1
Options presented:
a. $0.25
b. $0.26
c. $0.27
d. $0.28
Due to the test being timed I would appreciate it if you could show me a way to solve this problem in the quickest way possible? (along with step-by-step processes/formulas) I am not a math major, and I would appreciate any help you could offer. :)
Answer by greenestamps(13200)   (Show Source):
You can put this solution on YOUR website!
Use the fact that the quarters, dimes, and nickels together can make only totals that are multiples of 5 cents. That means...
a) To make 25 cents, you need to use 0 pennies. That means only quarters, dimes, and nickels. Obviously you can't use the quarter, because that is 25 cents by itself. So can you make 25 cents using four coins that are either dimes or nickels?
b) To make a total of 26 cents, you need to use 1 penny. That leaves 25 cents to be made using 3 coins, so again you need to do it with only dimes and nickels. Can you do that?
c) To make a total of 27 cents, you need to use 2 pennies, leaving 25 cents to be made with 2 other coins. That's not going to work....
d) To make a total of 28 cents, you need to use 3 pennies, leaving 25 cents to be made using only 1 coin. That solution is easy.
So you can make totals of 25 or 26 or 28 cents, but not 27 cents.
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