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Chapter 0: Problem 55

You have 35 hits in 140 times at bat. Your batting average is \(\frac{35}{140},\) or \(0.25 .\) How many consecutive hits must you get to increase your batting average to \(0.30 ?\)

Short Answer

Expert verified
You will need to get 10 consecutive hits to increase your batting average to 0.30.

Step by step solution

01

Define the problem

Let \( x \) denote the number of consecutive hits we are looking for. We don't know the value of \( x \) yet. The total number of at bats would then be \( 140 + x \), as the player will have \( x \) more attempts. Hence the total number of hits will be \( 35 + x \).
02

Formulate an equation

Since batting average is the number of hits divided by the number of at bats, let's express the batting average of 0.30 as an equation, i.e., \( \frac{35 + x}{140 + x} = 0.30 \).
03

Solve the equation

Now solve the equation for \( x \). First, cross-multiply to clear the fraction: \( (35 + x) * 1 = 0.30 * (140 + x) \). This simplifies to \( 35 + x = 42 + 0.30x \). Bring the \( x \) terms to one side and the number to the other gives \( 0.70x = 7 \). Divide by 0.70 on both sides gives \( x = 10 \).

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