If you spend $9.74 in how many ways can you receive change for a ten-dollar bill

Question

solomonzelman · Answer

well, the change you get is 26 cents.

So, way 1.    `1 quarter` + ` penny`

way 2.    `2 dimes` + `1 nickle` + ` penny`

way 3.    `1 dime` + `3 nickles` + ` penny`

way 4.     `5 nickles` + ` penny`

solomonzelman · Answer

So I think there are 4 ways.

anonymous · Answer

no sir there is more :) theres 26 pennies also

anonymous · Answer

i think that is it i cant think of anymore

anonymous · Answer

wait 16 pennies 1 nickel 
16 pennies 1 dime

anonymous · Answer

2nickles 16 pennies

anonymous · Answer

4 nickles 6 pennies

solomonzelman · Answer

my bad


So, way 1.    `1 quarter` +  `penny`

way 2.   ` 2 dimes` + `1 nickle` +  `penny`

way 3.   ` 2 dimes` +   `6 pennies`

way 4.    `1 dime` + `3 nickles` +  `penny`

way 5.    `1 dime` + `2 nickles` +  `6 pennies`

way 6.    `1 dime` + `1 nickles` +  `11 pennies`

way 7.    `1 dime` +   `16 pennies`

way 8.     `5 nickles` +  `1 penny`

way 9.     `4 nickles` +  `6 pennies`

way 10.     `3 nickles` +  `11 pennies`

way 11.     `2 nickles` +  `16 pennies`

way 12.     `1 nickles` +  `21 pennies`

way 12.       `26 pennies`

solomonzelman · Answer

I am reducing, first getting all patterns with quarters, then all patterns with dimes, then with nickles and then till I get the way 13, with 26 pennies.

solomonzelman · Answer

(The last one is way 13, not way 12)

jim_thompson5910 · Answer

SolomonZelman beat me to it, but I might as well post what I wrote


$10 - $9.74 = $0.26 = 26 cents


There are 13 ways to make 26 cents



1 penny + 1 quarter = 1*1 + 1*25 = 26 cents (2 coins)
1 penny + 1 nickel + 2 dimes = 1 + 5 + 2*10 = 26 cents (4 coins)
1 penny + 3 nickels + 1 dime = 1*1 + 3*5 + 1*10 = 26 cents (4 coins)
1 penny + 5 nickels = 1*1 + 5*5 = 26 cents (6 coins)
6 pennies + 2 dimes = 6*1 + 2*10 = 26 cents (8 coins)
6 pennies + 2 nickels + 1 dime = 6*1 + 2*5 + 1*10 = 26 cents (9 coins)
6 pennies + 4 nickels = 6*1 + 4*5 = 26 cents (10 coins)
11 pennies + 1 nickel + 1 dime = 11*1 + 1*5 + 1*10 = 26 cents (13 coins)
11 pennies + 3 nickels = 11*1 + 3*5 = 26 cents (14 coins)
16 pennies + 1 dime = 16*1 + 1*10 = 26 cents (17 coins)
16 pennies + 2 nickels = 16*1 + 2*5 = 26 cents (18 coins)
21 pennies + 1 nickel = 21*1 + 1*5 = 26 cents (22 coins)
26 pennies = 26*1 = 26 cents (26 coins)

solomonzelman · Answer

reducing the other direction :) I like this approach :)

anonymous · Answer

Lol thanks you guys. I appreciate it.