Frank had 3b baseball cards, and his brother had b baseball cards. They combined their cards, and then gave away 2b cards. The expression below shows how many they had left.

Question

Which of the following is another expression that could be used to get the same result, and what does it represent?
A.
4b - 2. This represents that Frank and his brother had 4b - 2 cards left.
B.
2b. This represents that Frank and his brother had 2b cards left.
C.
2 - b. This represents that Frank and his brother had 2 - b cards left.
D.
4b - 3b. This represents that Frank and his brother had 4b - 3b cards left.
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Answer 1

Let's start by determining how many baseball cards Frank and his brother had initially and how many they had left after giving away some cards.

1. Frank had \(3b\) baseball cards.
2. His brother had \(b\) baseball cards.

When they combine their cards:

\[ 3b + b = 4b \]

After combining their cards, they gave away \(2b\) cards. So, the number of cards they had left can be calculated as:

\[ 4b - 2b = 2b \]

Now, looking at the options provided:

A. \(4b - 2\): This represents that Frank and his brother had \(4b - 2\) cards left. \(4b - 2\) would not be correct because they had \(2b\) left after giving away \(2b\).

B. \(2b\): This represents that Frank and his brother had \(2b\) cards left. This is correct because it matches the result we calculated.

C. \(2 - b\): This represents that Frank and his brother had \(2 - b\) cards left. This is incorrect because it doesn’t match our calculated result.

D. \(4b - 3b\): This represents that Frank and his brother had \(4b - 3b\) cards left. Simplifying this gives \(b\), which is also incorrect based on our calculation.

Therefore, the correct option is:

B. \(2b\). This represents that Frank and his brother had \(2b\) cards left.