Question

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, must he hit this season to qualify?
H+22/6_>108
H+108/6_>22
H+108/6>22
H+22/6>108

Answer 1

Answer:

B. $\frac{H+108}{6}\geq 22$

Sam must hit at least 24 runs in 6th season to qualify for the home run trophy.

Step-by-step explanation:  

Let H be number of runs Sam hits in 6th season.  

We have been given that 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.

Let us find the number of runs scored by Sam adding the number of hits in his past 5 seasons.  

$\text{5 season score of Sam}=24+20+23+20+21=108$

We are told that to qualify for the home run trophy he must average at least 22 home runs in 6 seasons. So to qualify this season Sam's average must be greater than or equal to 22.

We can represent this information in an inequality as:

$\frac{H+108}{6}\geq 22$

Let us solve our inequality to find the least number of runs Sam must hit to qualify.

Multiplying both sides of our inequality by 6 we will get,

$6\times \frac{H+108}{6}\geq 6\times22$

$H+108\geq 132$  

$H\geq 132-108$

$H\geq 24$

Therefore, Sam must hit at least 24 runs this 6th season to qualify for the home run trophy.