Grace's average bowling score over the past 6 games is 150. If she wants to raise her average score by `10%,` and she has two more games remaining in the season, what must her average score on the last two games be ?

Answer

To solve the problem step by step, we will follow the reasoning provided in the video transcript.

### Step 1: Determine Grace's current average score
Grace's average bowling score over the past 6 games is given as 150.

### Step 2: Calculate the target average score
Grace wants to raise her average score by 10%. To find the new average:
\[ \text{New Average} = \text{Current Average} + \left(\text{Current Average} \times \frac{10}{100}\right) \]
\[ \text{New Average} = 150 + \left(150 \times 0.10\right) = 150 + 15 = 165 \]

### Step 3: Calculate the total score for the first 6 games
The total score from the first 6 games can be calculated as:
\[ \text{Total Score for 6 games} = \text{Average} \times \text{Number of Games} = 150 \times 6 = 900 \]

### Step 4: Set up the equation for the last two games
Let \( x \) be the average score Grace needs in the last two games. The total score for the last two games will then be:
\[ \text{Total Score for last 2 games} = 2 \times x \]

### Step 5: Calculate the total score for all 8 games
The total score for all 8 games will be:
\[ \text{Total Score for 8 games} = \text{Total Score for 6 games} + \text{Total Score for last 2 games} = 900 + 2x \]

### Step 6: Set up the average equation for all 8 games
The average score for all 8 games should equal the new average (165):
\[ \frac{900 + 2x}{8} = 165 \]

### Step 7: Solve the equation
To eliminate the fraction, multiply both sides by 8:
\[ 900 + 2x = 165 \times 8 \]
Calculating the right side:
\[ 165 \times 8 = 1320 \]
So the equation becomes:
\[ 900 + 2x = 1320 \]
Now, isolate \( 2x \):
\[ 2x = 1320 - 900 \]
\[ 2x = 420 \]
Now, divide by 2 to find \( x \):
\[ x = \frac{420}{2} = 210 \]

### Conclusion
Grace must score an average of **210** in her last two games to achieve her goal.

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