Frank had 4b 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

4b + b - 2b

Which of the following is another expression that could be used to get the same result, and what does it represent?
A.
5b - 2. This represents that Frank and his brother had 5b - 2 cards left.
B.
3b. This represents that Frank and his brother had 3b cards left.
C.
5b - 3b. This represents that Frank and his brother had 5b - 3b cards left.
D.
3 - b. This represents that Frank and his brother had 3 - b cards left.

Answer 1

To simplify the original expression \(4b + b - 2b\):

1. Combine the like terms: \(4b + b = 5b\)
2. Then subtract \(2b\): \(5b - 2b = 3b\)

So, they had \(3b\) cards left after giving away \(2b\) cards.

Now, let's evaluate the options:

A. \(5b - 2\). This is not equivalent to \(3b\). The expression and the representation are incorrect.

B. \(3b\). This is exactly equal to the result we obtained. So this is correct.

C. \(5b - 3b\). Simplifying this gives \(2b\), which is not equal to \(3b\). So this is incorrect.

D. \(3 - b\). This cannot represent the total number of cards left, as it doesn’t match our result and does not represent their remaining cards correctly. So this is incorrect.

The correct answer is B. \(3b\). This represents that Frank and his brother had \(3b\) cards left.