Let's solve each problem and match the answers to the corresponding letters to complete the riddle.

1. The concession stand made a profit of 135 on Saturday and lost $12 on Sunday. How much profit did the concession stand make over the weekend?
   \[135 - 12 = 123\]
   • Answer: \(H\) (123)
2. \(- 18 - ( - 13) \)
   \[- 18 + 13 = - 5\]
   • Answer: \(U\) or \(N\) or \(A\) (-5)
3. \(9 - ( - 21) \)
   \[9 + 21 = 30\]
   • Answer: \(I\) (30)
4. Rita owed her brother 15. After her birthday, she was able to pay him back and still had $45. How much money did Rita receive for her birthday?
   \[15 + 45 = 60\]
   • Answer: \(R\) (60)
5. \(- 35 + 12\)
   \[- 35 + 12 = - 23\]
   • Answer: \(E\) (-23)
6. \(17 - ( - 25) \)
   \[17 + 25 = 42\]
   • Answer: \(T\) (42)
7. Mercury has a freezing point of -38°F. Water has a freezing point of 32°F. What is the difference?
   \[32 - ( - 38) = 32 + 38 = 70\]
   • Answer: \(Q\) (70)
8. \(- 40 - ( - 16) \)
   \[- 40 + 16 = - 24\]
   • Answer: \(O\) (-24)
9. \(19 - 24\)
   \[19 - 24 = - 5\]
   • Answer: \(U\) or \(N\) or \(A\) (-5)
10. The winner of a card game is the person closest to zero. The second place player was eight points behind. If the winner has a score of -3, then what was the score for the second place?
    \[- 3 - 8 = - 11\]
    • Answer: \(S\) (-11)

Supplemental Knowledge

Subtracting integers can be thought of as adding their opposite; subtracting a negative number would equate to adding its positive counterpart, for instance. This concept can help solve real world scenarios where quantities increase or decrease, such as gains/losses situations and temperature changes.
For instance, if you have \(- 5 - ( - 3) \), this can be rewritten as \(- 5 + 3\). Similarly, \(7 - ( - 2) \) becomes \(7 + 2\).

Real-World Applications

Understood how to subtract integers can be invaluable when applied in various real-life circumstances, for instance managing finances involves the task of calculating net gains or losses over time if spending and receiving income on separate days requires you to accurately compute total balance calculations. Knowing how to accurately compute this total sum balance calculation is imperative if this scenario applies.

Mastering integer operations can significantly enhance your problem-solving skills in both academic and everyday contexts. At UpStudy, we provide comprehensive resources and tools to help you understand and apply these concepts effectively.
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