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
[tex]y=\dfrac{3}{4}x-1~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
and
[tex]x+y=153\\\\\Rightarrow x+\dfrac{3}{4}x-1=153\\\\\\\Rightarrow \dfrac{7}{4}x=154\\\\\Rightarrow \dfrac{x}{4}=22\\\\\Rightarrow x=22\times4\\\\\Rightarrow x=88.[/tex]
From equation (i), we get
[tex]y=\dfrac{3}{4}\times88-1=66-1=65.[/tex]
Thus, Kate's score is 65.
