Kalai threw a ball at a hoop 30 times. One point was scored when the ball passed through the hoop and one point was deducted when the bali did not. For Kalai's first 25 throws, the ball passed through the hoop 20 times. (a) What was Kalai's score from the first 25 throws? (b) At the end of 30 throws, Kalai scored 18 points. How many times did the ball pass through the hoop for her last 5 throws?

From the first 25 throws, Kalai scored 20 points for the successful shots that went through the hoop. However, she missed 5 shots, which means 5 points were deducted. So, to calculate her score, we take the successful shots minus the missed ones: \(20 - 5 = 15\). Thus, Kalai's score from the first 25 throws is 15 points. For the last 5 throws, we know Kalai's total score is 18 points. With 15 points already scored from the first 25 throws, that leaves 3 points from the last 5 throws. Since each successful shot adds a point and each miss deducts a point, we can set up the equation: \( x - (5 - x) = 3 \), where \( x \) is the number of successful throws. Solving for \( x \) yields \( 2x - 5 = 3 \), or \( 2x = 8 \), so \( x = 4 \). Therefore, Kalai passed the ball through the hoop 4 times in her last 5 throws.