2008 iTest Problems/Problem 22

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Problem

Tony plays a game in which he takes $40$ nickels out of a roll and tosses them one at a time toward his desk where his change jar sits. He awards himself $5$ points for each nickel that lands in the jar, and takes away $2$ points from his score for each nickel that hits the ground. After Tony is done tossing all $40$ nickels, he computes $88$ as his score. Find the greatest number of nickels he could have successfully tossed into the jar.

Solution

Let $x$ be the number of successful tosses. We can write an equation based on the scores. \[5x-2(40-x) = 88\] Remember to distribute the negative when using the Distributive Property. \[5x-80+2x=88\] \[7x=168\] \[x = 24\] If Tony did more than $24$ successful tosses, the unsuccessful tosses would decrease, and the score would increase. Thus, the greatest number of nickels tossed into the jar is $\boxed{24}$.

See Also

2008 iTest (Problems)
Preceded by:
Problem 21
Followed by:
Problem 23
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