Direct Variation

Question

A pitcher’s earned-run average E varies directly as the number R of earned runs allowed and inversely
as the number I of innings pitched. In 2010, Bronson Arroyo of the Cincinnati Reds had an earned-run
average of 3.89. He gave up 93 earned runs in 215.2 innings. How many earned runs would he have
given up had he pitched 238 innings with the same average? Round to the nearest whole number.

Answer 1

215.2/9 = 23.9111...

total innings divided by 9 innings per game

93/23.9111...= 3.89 ERA

238/9 = 26.444....

x/26.444... = 3.89

x = 3.89(26.444...) = 102.86888... = about 103 earned runs