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?

The pitcher would have 107 earned runs

Step-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 ∝

- 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 ∝

∴ , 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

∴

- 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

∵ E = 2.92 (same average)

∵ I = 330 innings

- We need to find the number of earned runs R

∴  

- 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

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