2008 iTest Problems/Problem 22

Revision as of 20:18, 23 June 2018 by Rockmanex3 (talk | contribs) (Created page with "==Problem== Tony plays a game in which he takes <math>40</math> nickels out of a roll and tosses them one at a time toward his desk where his change jar sits. He awards himse...")
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)

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
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 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100
Invalid username
Login to AoPS