Sarah's bowling score was 40 points more than Greg's, and the average of their two scores was 102. What was Sarah's score? (Recall that the average of two numbers is their sum divided by 2.)
The average of their scores is halfway between their scores.  Thus, since their scores differ by 40, and Sarah's score is higher, her score is $102+\frac{40}{2} = \boxed{122}$.

You can do this more precisely by calling Sarah's score $x$, and Greg's score is therefore $x - 40$.  Taking an average: $x - 20 = 102$, and thus, $x = 122$.
122
Level 3
Prealgebra
Problem: Sarah's bowling score was 40 points more than Greg's, and the average of their two scores was 102. What was Sarah's score? (Recall that the average of two numbers is their sum divided by 2.)
Solution:<|START_OF_LATENT|><|PRIOR_PREFIX|>To find Sarah's score, let S represent Sarah's score and G represent Greg's score. According to the problem, we know two key pieces of information: 

1. Sarah's score is 40 points more than Greg's score, which can be expressed as the equation: S = G + 40.
2. The average of their scores is 102, which means the sum of their scores divided by 2 equals 102. This can be expressed as: (S + G) / 2 = 102.

To eliminate the fraction in the average equation, we can multiply both sides by 2, leading to: S + G = 204.

Now we have a system of two equations:
1. S = G + 40
2. S + G = 204

Next, we can substitute the first equation into the second equation. Replacing S in the second equation gives us: (G + 40) + G = 204. 

Combining like terms results in: 2G + 40 = 204. 

To isolate G, we subtract 40 from both sides: 2G = 164. 

Dividing both sides by 2 yields: G = 82. 

Now that we have Greg's score, we can find Sarah's score using the first equation: S = G + 40. Substituting G = 82 into this equation gives us: S = 82 + 40, which simplifies to S = 122.

Thus, Sarah's score is 122.<|END_OF_LATENT|> The final answer is $122$.