Answer:
Step-by-step explanation:
We can write two equations in the two unknowns using the given relations. Let g and b represent the costs of a round of golf and a turn in the batting cage, respectively. 
   5g +4b = 60 . . . . . Sylvester's expense
   3g +6b = 45 . . . . . Lin's expense
Dividing the second equation by 3 gives ...
   g +2b = 15   ⇒   2b = 15 -g
Substituting into the first equation, we have ...
   5g +2(2b) = 60
   5g +2(15 -g) = 60 . . . . . substitute for 2b
   3g = 30 . . . . . . . . . subtract 30, collect terms
   g = 10 . . . . . . . divide by 3
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   2b = 15 -10 = 5 . . . . use the value of g to find b
   b = 2.5 . . . . . . . . divide by 2
Mini golf costs $10 per round; batting cages cost $2.50 per turn.