Difference between revisions of "2019 AMC 10B Problems/Problem 7"
| Line 9: | Line 9: | ||
==Solution 1== | ==Solution 1== | ||
| − | If he has enough money to buy 12 pieces of red candy, 14 pieces of green candy, and 15 pieces of blue candy, then the least money he can have is <math>lcm(12,14,15)</math> = 420. Since a piece of purple candy costs 20 cents, the least value of n can be <math>\frac{420}{20} \implies \boxed{\textbf{(B)} 21}</math> | + | If he has enough money to buy 12 pieces of red candy, 14 pieces of green candy, and 15 pieces of blue candy, then the least money he can have is <math>\lcm{(12,14,15)}</math> = 420. Since a piece of purple candy costs 20 cents, the least value of n can be <math>\frac{420}{20} \implies \boxed{\textbf{(B) } 21}</math> |
==Solution 2== | ==Solution 2== | ||
| − | We simply need to find a value of <math>20n</math> that divides 12, 14, and 15. <math>20*18</math> divides 12 and 15, but not 14. <math>20*21</math> successfully divides 12, 14 and 15, meaning that we have exact change (in this case, 420 cents) to buy each type of candy, so the minimum value of <math> | + | We simply need to find a value of <math>20n</math> that divides 12, 14, and 15. <math>20*18</math> divides 12 and 15, but not 14. <math>20*21</math> successfully divides 12, 14 and 15, meaning that we have exact change (in this case, 420 cents) to buy each type of candy, so the minimum value of <math>n</math> is <math>\boxed{\textbf{(B) } 21}</math>. |
| − | |||
| − | |||
| − | |||
==See Also== | ==See Also== | ||
Revision as of 22:40, 16 February 2019
- The following problem is from both the 2019 AMC 10B #7 and 2019 AMC 12B #5, so both problems redirect to this page.
Contents
Problem
Each piece of candy in a store costs a whole number of cents. Casper has exactly enough money to buy either 12 pieces of red candy, 14 pieces of green candy, 15 pieces of blue candy, or 
pieces of purple candy. A piece of purple candy costs 20 cents. What is the smallest possible value of ?
Solution 1
If he has enough money to buy 12 pieces of red candy, 14 pieces of green candy, and 15 pieces of blue candy, then the least money he can have is $\lcm{(12,14,15)}$ (Error compiling LaTeX. Unknown error_msg) = 420. Since a piece of purple candy costs 20 cents, the least value of n can be 
Solution 2
We simply need to find a value of 
that divides 12, 14, and 15. 
divides 12 and 15, but not 14. 
successfully divides 12, 14 and 15, meaning that we have exact change (in this case, 420 cents) to buy each type of candy, so the minimum value of is 
.
See Also
| 2019 AMC 10B (Problems • Answer Key • Resources) | ||
| Preceded by Problem 6 |
Followed by Problem 8 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
| All AMC 10 Problems and Solutions | ||
| 2019 AMC 12B (Problems • Answer Key • Resources) | |
| Preceded by Problem 4 |
Followed by Problem 6 |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | |
| All AMC 12 Problems and Solutions | |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
SUB2PEWDS
