Elena and Kiran are playing a board game. After one round, Elena says, "You earned so many more points than I did.

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If you earned 4 more points, your score would be thrice mine!" 

Kiran says, "Oh, I don't think I did that much better. I only scored 8 points higher than you did."

  1. Write a system of equations to represent each student's comment. Be sure to specify what your variables represent.
  2. If both students were correct, how many points did each student score? Show your reasoning.

Sangeetha Pulapaka

Let x be the points Elena has and y be the points Kiran has.

  1. Elena says that if Kiran would have earned four more points, she would have scored thrice as hers. The equation to represent this will be 3x = y + 4. Kiran says that she scored 8 points higher than Elena. The equation to represent this will be y = x+8.
  2. Assuming both students are correct, we solve these system of equations by substitution method (easy) as shown. Isolate y in the first equation 3x = y + 4 to get y = 3x - 4. This as you know is in the slope-intercept form. The second equation is y = x+8. Equate these across each other to get 3x - 4 = x + 8. Solve for x to get x = 6. Plug in this in equation 1 to get y = 3(6) - 4 = 18 - 4 = 14. So, Elena has 6 points and Kiran has 14.