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Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.Grayson went to play miniature golf on Monday, when it cost to rent the club and ball, plus per game. Warren went Thursday, paying per game, plus rental fees of . By coincidence, they played the same number of games for the same total cost. How much did each one spend? How many games did each one play?Grayson and Warren each spent _____ and played _____ games.
Full solution
Q. Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.Grayson went to play miniature golf on Monday, when it cost to rent the club and ball, plus per game. Warren went Thursday, paying per game, plus rental fees of . By coincidence, they played the same number of games for the same total cost. How much did each one spend? How many games did each one play?Grayson and Warren each spent _____ and played _____ games.
- Define Variables: Let's define the variables:Let be the number of games played by both Grayson and Warren.Let be the total cost for both Grayson and Warren.Now, we can write the equations based on the given information:For Grayson: For Warren:
- Write Equations: We can now write the system of equations as follows:For Grayson: For Warren:
- Set Equations Equal: To solve the system using substitution, we can set the two equations equal to each other since they both equal :
- Solve for x: Now, we solve for x:
- Substitute : Now that we have the value of , we can substitute it back into one of the original equations to find . We'll use Grayson's equation:
- Final Results: We have found that , the number of games played, is , and , the total cost for both Grayson and Warren, is \(\(19\))\(. So, Grayson and Warren each spent \$(19) and played \)\(3\) games.
