Question

1. a player has a slugging percentage of 0.500 and has 20 doubles, 5 triples, and 10 home runs in 200 at-bats. how many singles did they hit?

Explanation:

Step1: Recall slugging percentage formula

Slugging percentage (SLG) is calculated as $\frac{\text{Total Bases}}{\text{At - Bats}}$, where Total Bases $= 1\times\text{Singles}+ 2\times\text{Doubles}+3\times\text{Triples}+4\times\text{Home Runs}$. Let the number of singles be $x$.

Step2: Calculate total bases from known hits

Doubles: $2\times20 = 40$, Triples: $3\times5=15$, Home Runs: $4\times10 = 40$. So total bases from non - single hits is $40 + 15+40=95$. Total bases from all hits is $x + 95$.

Step3: Use slugging percentage formula

We know SLG $= 0.500$ and At - Bats $= 200$. So $\frac{x + 95}{200}=0.500$.
Multiply both sides by 200: $x + 95=0.500\times200=100$.
Subtract 95 from both sides: $x=100 - 95 = 5$.

Answer:

The player hit 5 singles.