Question

laura is bowling 5 games. her first 4 scores were 146, 120, 118, and 122. to end up with an average score of at least 131, what is the smallest score laura will need in the fifth game? 136 149 258

Explanation:

Step1: Calculate the total score needed for 5 games

The formula for the average $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}$. Here, $n = 5$ and $\bar{x}\geq131$. So the total score $S$ for 5 games should satisfy $S\geq131\times5$.
$$S\geq655$$

Step2: Calculate the sum of the first 4 - game scores

Let the scores of the first 4 games be $x_1 = 146$, $x_2=120$, $x_3 = 118$, $x_4=122$. Then the sum of the first 4 - game scores $S_4=x_1 + x_2+x_3+x_4$.
$$S_4=146 + 120+118+122=506$$

Step3: Find the score of the fifth game

Let the score of the fifth game be $x_5$. Since $S=S_4 + x_5\geq655$, then $x_5\geq655 - S_4$.
Substitute $S_4 = 506$ into the inequality: $x_5\geq655-506$.
$$x_5\geq149$$

Answer:

149