Difference between revisions of "2021 JMPSC Problems/Problem 2"
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== Problem == | == Problem == | ||
| − | Brady has an unlimited supply of quarters (<math>0.25), dimes (</math>0.10), nickels (<math>0.05), and pennies (</math>0.01). What is the least number (quantity, not type) of coins Brady can use to pay off [ | + | Brady has an unlimited supply of quarters (<math>0.25), dimes (</math>0.10), nickels (<math>0.05), and pennies (</math>0.01). What is the least number (quantity, not type) of coins Brady can use to pay off [verbatim]<math>[/verbatim]</math>2.78<math>? |
== Solution == | == Solution == | ||
| − | To minimize the number of coins, we need to maximize the amount of high-valued coins we use. 11 quarters are worth [ | + | To minimize the number of coins, we need to maximize the amount of high-valued coins we use. 11 quarters are worth [verbatim]</math>[/verbatim]<math>2.75</math>, which is the most quarters we can use to get a value less than or equal to [verbatim]<math>[/verbatim]</math>2.78<math>. Finally, we can add 3 pennies to get a total of [verbatim]</math>[/verbatim]<math>2.87</math>, so the answer is <math>11+3=14</math>. |
Revision as of 18:25, 10 July 2021
Problem
Brady has an unlimited supply of quarters (
0.10), nickels (
0.01). What is the least number (quantity, not type) of coins Brady can use to pay off [verbatim]![$[/verbatim]$](http://latex.artofproblemsolving.com/3/6/3/3631009f7dbbe9902a45896f2b4a164b938a128a.png)
2.78$?
== Solution ==
To minimize the number of coins, we need to maximize the amount of high-valued coins we use. 11 quarters are worth [verbatim]$ (Error compiling LaTeX. Unknown error_msg)[/verbatim]
, which is the most quarters we can use to get a value less than or equal to [verbatim]2.78![$. Finally, we can add 3 pennies to get a total of [verbatim]$](http://latex.artofproblemsolving.com/a/3/d/a3d6cd0f668c09a913f962bd67892fb75f27ac7f.png)
[/verbatim]
, so the answer is 
.
