Michael is participating in a 5-day cross-country biking challenge. He biked for \( 49,51,64 \), and 53 miles on the first four days. How many miles does he need to bike on the last day so that his average (mean) is 54 miles per day? miles

To find out how many miles Michael needs to bike on the last day so that his average (mean) is 54 miles per day, we can use the formula for the mean: \[ \text{Mean} = \frac{\text{Total miles}}{\text{Number of days}} \] Given that Michael biked for 49, 51, 64, and 53 miles on the first four days, we can calculate the total miles he has biked so far: \[ \text{Total miles} = 49 + 51 + 64 + 53 = 217 \text{ miles} \] Since Michael wants his average to be 54 miles per day, we can set up the equation: \[ \frac{217 + x}{5} = 54 \] where \( x \) is the number of miles he needs to bike on the last day. Now, we can solve for \( x \) to find out how many miles Michael needs to bike on the last day. Solve the equation by following steps: - step0: Solve for \(x\): \(\frac{217+x}{5}=54\) - step1: Cross multiply: \(217+x=5\times 54\) - step2: Simplify the equation: \(217+x=270\) - step3: Move the constant to the right side: \(x=270-217\) - step4: Subtract the numbers: \(x=53\) Michael needs to bike 53 miles on the last day so that his average (mean) is 54 miles per day.