Question
Tim bought 5 new baseball trading cards to add to his collection. The next day his dog ate half of his collection. There are now only 32 cards left. How many cards did Tim start with?
Ask by Ayala Chan. in the United States
Mar 13,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
Tim originally had 59 cards.
Solution
1. Let \( x \) be the number of cards Tim originally had.
2. After buying 5 cards, Tim's total becomes:
\[
x + 5
\]
3. His dog ate half of the collection, leaving:
\[
\frac{x + 5}{2}
\]
and we know this equals 32:
\[
\frac{x + 5}{2} = 32
\]
4. Multiply both sides by 2 to eliminate the fraction:
\[
x + 5 = 64
\]
5. Subtract 5 from both sides to solve for \( x \):
\[
x = 64 - 5 = 59
\]
Tim originally had \( 59 \) cards.
Answered by UpStudy AI and reviewed by a Professional Tutor
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Simplify this solution Bonus Knowledge
Tim started with 32 cards left after his dog ate half of his collection. Since his dog consumed half, he must have originally had 64 cards before the mishap. Adding the 5 new cards he bought brings the initial total to 59 cards. So, Tim started with 59 baseball trading cards. Remember, when you encounter problems like this, it's good to break it down step by step. First, determine how many cards were remaining before the dog ate them, and then include any new cards added to find the total. A common mistake is to forget to account for the new cards when calculating the original total!
