Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks. Zane went to play miniature golf on Monday, when it cost $16 to rent the club and ball, plus $1 per game. Omar went Thursday, paying $2 per game, plus rental fees of $6. 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? Zane and Omar each spent $_____ and played _____ games.

Question

Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.  Zane went to play miniature golf on Monday, when it cost $16 to rent the club and ball, plus $1 per game. Omar went Thursday, paying $2 per game, plus rental fees of $6. 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?   Zane and Omar each spent $_____ and played _____ games.

Bytelearn · Accepted Answer

Define variables: Let's define the variables for the system of equations. Let x represent the number of games played by each, and let y represent the total cost for each person.Zane's equation: For Zane, the cost is $16 for the rental plus $1 per game. So, the equation for Zane is: y = 16 + 1xOmar's equation: For Omar, the cost is $6 for the rental plus $2 per game. So, the equation for Omar is: y = 6 + 2xSet equations equal: Now we have a system of two equations: 1) y = 16 + x 2) y = 6 + 2x We can solve this system using substitution. Since both equations equal y, we can set them equal to each other: 16 + x = 6 + 2xSolve for x: Next, we solve for x by subtracting x from both sides of the equation: 16 + x - x = 6 + 2x - x 16 = 6 + xIsolate x: Now, subtract 6 from both sides to isolate x: 16 - 6 = 6 + x - 6 10 = xSubstitute x into equation: We found that x, the number of games played, is 10. Now we can substitute x back into either of the original equations to find y, the total cost. Let's use Zane's equation: y = 16 + 1x y = 16 + 1(10)Calculate Zane's cost: Calculate the total cost for Zane: y = 16 + 10 y = 26Calculate Omar's cost: Since Zane and Omar spent the same amount and played the same number of games, Omar also spent $26 and played 10 games.

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