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. A certain pitcher had an​ earned-run average of​ 2.92, giving up 85 earned runs in 262 innings. How many earned runs would the pitcher have given up having pitched 330 innings with the same​ average?

Answer:The pitcher would have 107 earned runsStep-by-step explanation:- The earned-run average is E- The number of earned runs is R- The number of innings pitched is I - E varies directly with R ⇒ E ∝ R- E is varies inversely with I ⇒ E ∝ [tex]\frac{1}{I}[/tex]- The earned average is 2.92 when giving up 85 earned runs in   262 innings- We need to find how many earned runs would the pitcher have given   up having pitched 330 innings with the same​ average∵ E ∝ R and E ∝ [tex]\frac{1}{I}[/tex]∴ [tex]E=\frac{kR}{I}[/tex] , where k is the constant of variation- To find the constant of variation k we must use the initial values of E,   R, and I∵ E = 2.92 , R = 85 and I = 262- Substitute these values in the equation above∴ [tex]2.92=\frac{k(85)}{262}[/tex]- Multiply both sides by 262∴ 765.04 = 85 k- Divide both sides by 85∴ k ≅ 9- Substitute the value of k in the equation∴ The equation is [tex]E=\frac{9R}{I}[/tex]∵ E = 2.92 (same average)∵ I = 330 innings- We need to find the number of earned runs R∴  [tex]2.92=\frac{9R}{330}[/tex]- Multiply both sides by 330∴ 963.6 = 9 R- Divide both sides by 9∴ R = 107.07 ≅ 107* The pitcher would have 107 earned runs