2008 iTest Problems/Problem 22
Problem
Tony plays a game in which he takes 
nickels out of a roll and tosses them one at a time toward his desk where his change jar sits. He awards himself 
points for each nickel that lands in the jar, and takes away 
points from his score for each nickel that hits the ground. After Tony is done tossing all nickels, he computes 
as his score. Find the greatest number of nickels he could have successfully tossed into the jar.
Solution
Let 
be the number of successful tosses. We can write an equation based on the scores.
![\[5x-2(40-x) = 88\]](http://latex.artofproblemsolving.com/7/c/5/7c545b36aee9f5f3702ee1f95ebd180be8fe0543.png)
Remember to distribute the negative when using the Distributive Property.
![\[5x-80+2x=88\]](http://latex.artofproblemsolving.com/c/c/5/cc53700b209dd275d72e9a0841505fe1ae457748.png)
![\[7x=168\]](http://latex.artofproblemsolving.com/b/1/a/b1a4be66d75c13d87766d654ee9e29b04231406f.png)
![\[x = 24\]](http://latex.artofproblemsolving.com/3/a/1/3a18002296f7b456494f9ce99f7182976021f733.png)
If Tony did more than 
successful tosses, the unsuccessful tosses would decrease, and the score would increase. Thus, the greatest number of nickels tossed into the jar is 
.
See Also
| 2008 iTest (Problems) | ||
| Preceded by: Problem 21 |
Followed by: Problem 23 | |
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