Question

question #12
use the information given to answer the question.
the total points scored by a schools junior varsity basketball team for each of the past 5 games are
120, 90, 112, 105, 88
the total points scored by the schools varsity basketball team for each of the past 4 games are 98, 108, 82, and 110.
how many points must the varsity basketball team score in their 5th game for the mean scores of both teams to be equal?
a 113 points
b 110 points
c 117 points
d 120 points

Explanation:

Step1: Calculate junior - varsity mean

The formula for the mean $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}$. For the junior - varsity team, $n = 5$, and $\sum_{i=1}^{5}x_{i}=120 + 90+112 + 105+88=515$. So the mean $\bar{x}_{1}=\frac{515}{5}=103$.

Step2: Let the score of the 5th varsity - game be $x$.

The sum of the varsity team's scores for the first 4 games is $98 + 108+82 + 110 = 398$. The mean of the varsity team's scores after 5 games should be equal to the mean of the junior - varsity team. So $\frac{398 + x}{5}=103$.

Step3: Solve for $x$.

Multiply both sides of the equation $\frac{398 + x}{5}=103$ by 5: $398+x = 103\times5=515$. Then subtract 398 from both sides: $x=515 - 398=117$.

Answer:

C. 117 points