Question

which inequality models this problem? sam wants to be named the greatest home run hitter of his baseball league. in the past 5 seasons he has hit 24, 20, 23, 20, and 21 home runs, respectively. to qualify for the home run trophy he must average at least 22 home runs in 6 seasons. how many home runs, h, must he hit this season to qualify? \\(\frac{h + 22}{6} \geq 108\\) \\(\frac{h + 22}{6} > 108\\) \\(\frac{h + 108}{6} > 22\\) \\(\frac{h + 108}{6} \geq 22\\)

Explanation:

Step1: Calculate total past home runs

$24 + 20 + 23 + 20 + 21 = 108$

Step2: Define average for 6 seasons

The total home runs over 6 seasons is $108 + h$, so the average is $\frac{108 + h}{6}$.

Step3: Set up the inequality

The average must be at least 22, so $\frac{h + 108}{6} \geq 22$.

Answer:

$\boldsymbol{\frac{h+108}{6} \geq 22}$ (the fourth option)