Question

laura is bowling 5 games. her first 4 scores were 108, 126, 91, and 92. to end up with an average score of at least 103, what is the smallest score laura will need in the fifth game? 102 208 98

Explanation:

Step1: Calculate the total score needed

The formula for the average $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}$. Here, $n = 5$ and $\bar{x}\geq103$. So the total score $\sum_{i=1}^{5}x_{i}\geq103\times5$.
$$\sum_{i = 1}^{5}x_{i}\geq515$$

Step2: Calculate the sum of the first - four scores

Let the first - four scores be $x_1 = 108$, $x_2=126$, $x_3 = 91$, $x_4 = 92$. Then $\sum_{i = 1}^{4}x_{i}=108 + 126+91 + 92$.
$$\sum_{i = 1}^{4}x_{i}=417$$

Step3: Find the fifth - game score

Let the fifth - game score be $x_5$. We know that $\sum_{i = 1}^{5}x_{i}=\sum_{i = 1}^{4}x_{i}+x_5$. From $\sum_{i = 1}^{5}x_{i}\geq515$ and $\sum_{i = 1}^{4}x_{i}=417$, we have $x_5\geq515-\sum_{i = 1}^{4}x_{i}$.
$$x_5\geq515 - 417$$
$$x_5\geq98$$

Answer:

98