(b) Paul's uncle gave him some white masks. The ratio of Paul's number of black masks to the number of white masks is now \( 1: 2 \). Find the number of white masks he received from his uncle.

Let the number of black masks Paul has be \( b \) and the number of white masks he received from his uncle be \( w \). According to the problem, the ratio of the number of black masks to the number of white masks is given as \( 1:2 \). This can be expressed mathematically as: \[ \frac{b}{w} = \frac{1}{2} \] From this ratio, we can express \( b \) in terms of \( w \): \[ b = \frac{1}{2}w \] This means that for every 2 white masks, Paul has 1 black mask. To find the number of white masks \( w \), we need additional information about the total number of masks or the number of black masks. However, since the problem does not provide that information, we can express the number of white masks in terms of the number of black masks. If we let \( w = 2k \) for some integer \( k \), then the number of black masks would be: \[ b = k \] Thus, the total number of masks Paul has is: \[ b + w = k + 2k = 3k \] Without additional information about the total number of masks or the number of black masks, we cannot determine a specific numerical value for \( w \). If you have any specific values or additional context, please provide that, and I can help you find the exact number of white masks. Otherwise, the number of white masks can be expressed as \( w = 2k \) for some integer \( k \).