Answer: Kate's score is 65.
Step-by-step explanation: Given that Kate's golf score was 1 less than three fourths of Greg's golf score and the sum of their scores was 153.
We are to find Kate's score.
Let x and y represents Greg's score and Kate's score respectively.
Then, according to the given information, we have

and

From equation (i), we get

Thus, Kate's score is 65.