Holly and melanie were playing a video game. the ratio of holly's score to melanie's score was 8: 3. after melanie scored 34 points, the ratio of their scores became 2: 5. what were their scores at the end?

They started with a ratio of 8:3.
Since we don't know the actual numbers, let's say their scores were originally 8x for Holly and 3x for Melanie.
Then Melanie scored 34 points, so her score became 3x + 34.
Holly's score remained the same at 8x.
The new ratio is 2:5, so

8x/(3x + 34) = 2/5

Now we solve the equation for x.

40x = 6x + 68

34x = 68

x = 2

With x, we can find the scores.

Holly ended up with 8x = 8 * 2 = 16
Melanie ended up with 3x + 34 = 3(2) + 34 = 40