Question
Bob has three times as many baseball cards as Bill. Together they have a total of 68 cards. How many cards does Bob have? cards
Ask by Mullins Wood. in the United States
Jan 15,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
Bob has 51 baseball cards.
Solution
Let's solve the problem step by step.
**Problem Statement:**
- Bob has **three times** as many baseball cards as Bill.
- Together, they **have a total of 68 cards**.
- **Question:** How many cards does Bob have?
**Let’s Define the Variables:**
- Let **\( B \)** represent the number of baseball cards Bill has.
- Therefore, **Bob has \( 3B \) cards** (since Bob has three times as many as Bill).
**Set Up the Equation:**
Together, Bill and Bob have 68 cards. So,
\[
B + 3B = 68
\]
**Combine Like Terms:**
\[
4B = 68
\]
**Solve for \( B \):**
\[
B = \frac{68}{4} = 17
\]
**Find the Number of Cards Bob Has:**
\[
\text{Bob's cards} = 3B = 3 \times 17 = 51
\]
**Answer:** Bob has **51** baseball cards.
Answered by UpStudy AI and reviewed by a Professional Tutor
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Simplify this solution Extra Insights
To solve this riddle, let's assign variables: let Bill have \( x \) cards. Therefore, Bob, having three times as many, has \( 3x \) cards. Together, their cards add up to 68, giving us the equation: \[ x + 3x = 68 \] This simplifies to \( 4x = 68 \). Dividing both sides by 4, we find \( x = 17 \). Thus, Bill has 17 cards, and Bob has \( 3 \times 17 = 51 \) cards! Go Bob with those cool cards! Now, if you encounter a similar problem where the variables are less obvious, try drawing a simple diagram or using colored markers to visualize the relationship. It helps avoid mixing up the numbers and keeps your problem organized. Happy calculating!
