Question

2.frank wants to have a bowling average of 215. the first 7 games he scored 159, 182, 225, 240, 198, 200, 230. what must he score in the 8th game to have an average of 215?

Explanation:

Step1: Recall the average formula

The formula for the average (mean) of a set of numbers is $\text{Average} = \frac{\text{Sum of all numbers}}{\text{Number of numbers}}$. Let $x$ be the score of the 8th game. The total number of games will be 8, and the desired average is 215. So we can write the equation: $\frac{159 + 182 + 225 + 240 + 198 + 200 + 230 + x}{8} = 215$.

Step2: Calculate the sum of the first 7 scores

First, we find the sum of the scores of the first 7 games: $159 + 182 + 225 + 240 + 198 + 200 + 230$. Let's calculate that step by step:
$159+182 = 341$;
$341+225 = 566$;
$566+240 = 806$;
$806+198 = 1004$;
$1004+200 = 1204$;
$1204+230 = 1434$.

Step3: Solve for x

Substitute the sum of the first 7 scores into the average equation: $\frac{1434 + x}{8} = 215$. Multiply both sides of the equation by 8 to get rid of the denominator: $1434 + x = 215\times8$. Calculate $215\times8 = 1720$. Then, subtract 1434 from both sides to solve for x: $x = 1720 - 1434$.

Step4: Calculate the value of x

$1720 - 1434 = 286$.

Answer:

286