Question

After 50 times at bat, a major league baseball player has a batting average of \(0.160 .\) How many consecutive hits must the player get to raise his batting average to \(0.250 ?\)

Short answer

The player must get 18 consecutive hits to raise his batting average to 0.250.

Step-by-step solution

Determine the initial number of hits

First, we need to determine the player's initial number of hits. We can do this by multiplying the player's current batting average by the number of times he has been at bat. So, \(0.160 * 50 = 8\) hits.

Setup the equation to find the number of needed consecutive hits

In order to find out how many consecutive hits the player needs, we can set up the equation: \((8 + x) / (50 + x) = 0.250\), where \(x\) is the unknown consecutive hits.

Solve the Equation

First expand the equation to \(8 + x = 0.250 * (50 + x)\), this simplifies to \(8 + x = 12.5 + 0.250x\). Solving this equation gives \(x = 18\).