Difference between revisions of "2021 JMPSC Problems/Problem 2"
Mathdreams (talk | contribs) |
Mathdreams (talk | contribs) |
||
| Line 1: | Line 1: | ||
== 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 <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 <math>\$2.75</math>, which is the most quarters we can use to get a value less than or equal to <math>\$2.78</math>. Finally, we can add 3 pennies to get a total of <math>\$2.87</math>, so the answer is <math>11+3=14</math>. |
Revision as of 19:28, 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 
?
Solution
To minimize the number of coins, we need to maximize the amount of high-valued coins we use. 11 quarters are worth 
, which is the most quarters we can use to get a value less than or equal to . Finally, we can add 3 pennies to get a total of 
, so the answer is 
.
