Final answer:
To find the number of bottles used at the race, subtract the number of bottles left after the race from the total number of bottles bought. In this case, the calculation is 192 - 34 = 158 bottles used.
Step-by-step explanation:
To find the number of bottles used at the race, we can subtract the number of bottles left after the race from the total number of bottles Coach Ramirez bought. Coach Ramirez bought 8 cases of bottled water, and there are 24 bottles in each case, so the total number of bottles he bought is 8 x 24 = 192 bottles. After the race, there were 34 bottles left, so the number of bottles used at the race is 192 - 34 = 158 bottles.