1. **State the problem:** Five people went to a restaurant. Four of them each spent $12 less than the average amount spent by all five together, and the fifth person spent $18 less than twice the average. We need to find the total amount spent by the fifth person. 2. **Define variables:** Let the average amount spent by all five people be $x$. 3. **Express amounts spent:** - Each of the four people spent $x - 12$. - The fifth person spent $2x - 18$. 4. **Write the equation for the total amount spent:** $$4(x - 12) + (2x - 18) = 5x$$ 5. **Simplify the equation:** $$4x - 48 + 2x - 18 = 5x$$ $$6x - 66 = 5x$$ 6. **Solve for $x$:** $$6x - 5x = 66$$ $$x = 66$$ 7. **Find the amount spent by the fifth person:** $$2x - 18 = 2(66) - 18 = 132 - 18 = 114$$ 8. **Check the options:** None of the options list 114 for the fifth person, so let's verify the problem statement carefully. **Re-examining the problem:** It says "Four of them spent $12 less than the average amount of money they spent together" and "the fifth person spent $18 less than twice the average." The average is for all five people. Let's check the total sum with $x=66$: - Four people: $4 imes (66 - 12) = 4 imes 54 = 216$ - Fifth person: $114$ - Total: $216 + 114 = 330$ Average: $330 / 5 = 66$, which matches $x$. 9. **Compare with options:** The options show repeated amounts for the first four people and a different amount for the fifth. Let's check which option matches the pattern: - Option 1: $56, 56, 56, 56, 58$ total $56*4 + 58 = 282$ average $282/5=56.4$ no - Option 2: $48, 48, 48, 48, 88$ total $48*4 + 88 = 280$ average $56$ no - Option 3: $52, 52, 52, 52, 72$ total $52*4 + 72 = 280$ average $56$ no - Option 4: $44, 44, 44, 44, 104$ total $44*4 + 104 = 280$ average $56$ no None match the average 66 we found. 10. **Check if the problem meant the average of the four people, not all five:** Let $y$ be the average of the four people. - Each of the four spent $y - 12$. - Fifth person spent $2y - 18$. Total spent: $$4(y - 12) + (2y - 18) = 4y - 48 + 2y - 18 = 6y - 66$$ Average of all five: $$\frac{6y - 66}{5} = y$$ Multiply both sides by 5: $$6y - 66 = 5y$$ $$6y - 5y = 66$$ $$y = 66$$ So average of four people is 66. Amounts: - Four people: $66 - 12 = 54$ - Fifth person: $2(66) - 18 = 132 - 18 = 114$ Total: $$4 imes 54 + 114 = 216 + 114 = 330$$ Average of all five: $$330 / 5 = 66$$ 11. **Conclusion:** The fifth person spent 114, which is not in the options. Possibly a typo in options or problem. **Final answer:** The fifth person spent $114$.