A baseball pitcher has pitched a total of 25 innings so far during the season and has allowed 18 runs. At this rate, how many runs, to the nearest hundredth, would he allow in nine innings? This number is called the pitcher’s earned run average, or ERA.
b. Randy Johnson of the Arizona Diamondbacks had an ERA of 2.64 in 2000. At that rate, how many runs would he be expected to allow in 100 innings pitched? Round your answer to the nearest whole number.
A. 18/25 = x/9
B. x/100 = 2.64/9
Solve for x.
To calculate the pitcher's earned run average (ERA), we need to divide the total runs allowed by the number of innings pitched.
In the first scenario, the pitcher has pitched 25 innings and allowed 18 runs. Therefore, the ERA can be calculated as follows:
ERA = Total runs allowed / Innings pitched
ERA = 18 runs / 25 innings
To find out how many runs the pitcher would allow in nine innings, we can use the ratio between the runs and innings from the given data.
Runs in 9 innings = ERA * 9
Substituting the given values:
Runs in 9 innings = (18 runs / 25 innings) * 9 innings
Calculating:
Runs in 9 innings ≈ 6.48
Therefore, the pitcher would be expected to allow approximately 6.48 runs in nine innings.
Now let's move on to the second scenario.
Randy Johnson had an ERA of 2.64 in 2000, which means he allowed 2.64 runs per inning pitched.
To determine how many runs he would be expected to allow in 100 innings, we can use the ratio between the runs and innings from the given data.
Runs in 100 innings = ERA * 100
Substituting the given values:
Runs in 100 innings = 2.64 runs per inning * 100 innings
Calculating:
Runs in 100 innings = 264
Therefore, Randy Johnson would be expected to allow approximately 264 runs in 100 innings pitched.