If you have a pocket full of change, what is the most amount of money you can have but still not have exact change for a dollar?
Also tell me how you know!! plz explain!!
web sit maybe???!!!
2007-12-15 06:13:44 · 9 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
I came up with two answers:
3 quarters, 4 dimes, 4 pennies
or
1 quarter, 9 dimes, 4 pennies
But either way it's $1.19.
How do I know? Mostly guess and check with a little logic thrown in. I'll explain how I came up with the first answer:
The most quarters possible is 3 because 4 would be exactly $1. The most dimes possible with three quarters is 4 because 2 quarters + 5 dimes = $1. You can't use any nickels because adding a nickel to 3 quarters would make 80 cents, and then you could only have 1 dime (80¢ + 2 dimes = $1). As for pennies, you can only have 4 because 5 would be equivalent to a nickel, which we already determined would reduce the number of possible dimes from 4 to 1.
See if you can use the same type of reasoning starting with 9 dimes.
2007-12-15 06:28:14 · answer #1 · answered by Meatball 2 · 1⤊ 0⤋
Let's try to prove an answer here.
A. Without loss of generality, there are no more than 4 pennies. If not, remove 5 pennies and replace them with a nickel; that doesn't affect whether you can make change for a dollar.
B. Without loss of generality, there is no more than 1 nickel. Same reasoning as before. If there were, you could replace two nickels with one dime without changing anything.
C. Without loss of generality, there are no more than 4 dimes, because otherwise you could replace 5 dimes by 2 quarters.
D. Obviously, there are no more than 3 quarters.
Note that without loss of generality, the amount of money OTHER than in quarters is no more than 49 cents (4 dimes plus 1 nickel plus 4 pennies).
As noted in earlier answers, there's at least one solution that reaches $1.19, namely 3 quarters, 4 dimes, 0 nickels, and 4 pennies. If that can be beat at all, it can be beat with the value of the quarters being more than $.70, since without loss of generality the value of the other coins is no more than $0.49. So you only have look at solutions with 3 quarters.
Any solution that involves no more than 3 quarters, no more than 4 dimes, no more than 1 nickel, and no more than 4 pennies, but beats $1.19, will indeed contain exactly 3 quarters, 4 dimes, and 1 nickel (leave out a quarter, dime, or nickel and you can't beat $1.19). But if it contains all those coins, there is change for a dollar.
Hence there is no solution that beats $1.19. Q.E.D.!!
2007-12-15 11:44:46 · answer #2 · answered by Curt Monash 7 · 1⤊ 0⤋
Gloria Macapagal Arroyo
2016-05-24 02:19:06 · answer #3 · answered by Anonymous · 0⤊ 0⤋
99 pennies, 99 coins but doesnt fit into a dollar
2007-12-15 10:20:51 · answer #4 · answered by jettica24 3 · 0⤊ 0⤋
100$
2007-12-15 06:17:26 · answer #5 · answered by (ƸӜƷ) 1 · 0⤊ 2⤋
99 cents
If you have a dollar in change, obviously you can change a dollar. If you have more than a dollar in change (for example $1.27, you keep $.27 and the rest is cange for a dollar.
2007-12-15 06:21:43 · answer #6 · answered by ironduke8159 7 · 1⤊ 2⤋
It might be three quarters and nine dimes. You have to maximize the amount (three quarters) and avoid counting to an exact dollar (9 dimes). Total is $1.65,
2007-12-15 06:18:31 · answer #7 · answered by Ken 7 · 0⤊ 4⤋
99 cents. i got it because it is not exactly a dollar you could have 99 cents
2007-12-15 06:17:49 · answer #8 · answered by Anonymous · 0⤊ 2⤋
$1.19
3 quarter
4 dimes
4 pennies
trial and error
2007-12-15 06:22:41 · answer #9 · answered by trent 3 · 1⤊ 0⤋