2005 iTest Problems/Problem 8

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Problem

Joe and Kathryn work part-time jobs at the local mall to make some money for college. Joe works at GameStop, while Kathryn works at Bath and Body Works. However, neither of them usually ever leaves on pay day without spending a healthy portion of their check at their own store, especially angering Joe’s parents, who think video games are for Neanderthals or children under $8$.

Joe makes $$8$ an hour, while Kathryn makes $$10$ an hour. Both work $20$ hours a week. Every week, Joe has a $20\%$ probability of purchasing a used $$25$ video game, and Kathryn has a $25\%$ probability of purchasing a $$30$ skin moisturizer. Find the expected value, in dollars, of their combined weekly “take-home pay.” (Take-home pay is total pay minus in-store spending.)

Solution 1

Since Joe makes 8 dollars per hour, he makes $8\cdot20=$160$ per week. Kathryn makes $10\cdot20=$200$ per week. Joe's expected spending per week, is $20\%\cdot25=$5$, and Kathryn's expected spending per week is $25\%\cdot30=$7.50$. Thus, their combined expected take-home pay is $160+200-5-7.50=\boxed{$347.50}$.

See Also

2005 iTest (Problems, Answer Key)
Preceded by:
Problem 7
Followed by:
Problem 9
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