Pinocchio told 32 lies in \( 42 \frac{1}{2} \) minutes. How many lies would he tell in 189 minutes if he told lies at the same rate?

To find out how many lies Pinocchio would tell in 189 minutes, we first need to determine his rate of lying per minute. Pinocchio told 32 lies in \( 42 \frac{1}{2} \) minutes. We can convert \( 42 \frac{1}{2} \) minutes into an improper fraction: \[ 42 \frac{1}{2} = 42 + \frac{1}{2} = \frac{84}{2} + \frac{1}{2} = \frac{85}{2} \text{ minutes} \] Next, we calculate the rate of lies per minute: \[ \text{Rate} = \frac{32 \text{ lies}}{\frac{85}{2} \text{ minutes}} = 32 \times \frac{2}{85} = \frac{64}{85} \text{ lies per minute} \] Now, we need to find out how many lies he would tell in 189 minutes at this rate: \[ \text{Lies in 189 minutes} = \text{Rate} \times \text{Time} = \frac{64}{85} \text{ lies per minute} \times 189 \text{ minutes} \] Calculating this gives: \[ \text{Lies in 189 minutes} = \frac{64 \times 189}{85} \] Now, we calculate \( 64 \times 189 \): \[ 64 \times 189 = 12144 \] Next, we divide by 85: \[ \frac{12144}{85} \] To perform the division, we can calculate: \[ 12144 \div 85 \approx 143.5 \] Since the number of lies must be a whole number, we round down to the nearest whole number: \[ \text{Lies in 189 minutes} = 143 \] Thus, the number of lies Pinocchio would tell in 189 minutes is \[ \boxed{143} \]