2. Liz received some money for her birthday. On Monday, she spent half of the money on a new video game; on Tuesday, she spent a third of what was left on a shirt; and on Wednesday, she spent a fourth of what was left on a new book. If she has $15 remaining. How much money did Liz receive for her birthday?
Answer: D
Liz received $60 for her birthday.
Liz spent her birthday money in a series of transactions, and after calculating the remaining amount, we find that the total amount she received was $60.
A) $360
This option is incorrect because if Liz had received $360, her spending pattern would not leave her with just $15 remaining. Half of $360 is $180, spending a third of that would leave her with much more than $15 after subsequent purchases.
B) $180
This option is also incorrect. Starting with $180, if Liz spent half, she would have $90 left. Spending a third of that on a shirt would leave her with $60, and spending a fourth of that on a book would leave her with more than $15, making this option unviable.
C) $120
Option C is incorrect as well. If Liz received $120, after spending half on a video game, she would have $60 remaining. Spending a third of that ($20) on a shirt would leave her with $40, and spending a fourth of $40 ($10) on a book would leave her with $30, again more than $15.
D) $60
This is the correct option. If Liz received $60, she spent half on a video game ($30), leaving her with $30. Spending a third of that ($10) on a shirt leaves her with $20, and spending a fourth of $20 ($5) on a book leaves her with exactly $15, matching the information provided in the question.
Conclusion
Liz's initial amount of $60 aligns perfectly with her spending pattern, resulting in the remaining balance of $15. All other options fail to correspond with the final amount after her expenditures, confirming that $60 is the only viable answer.