The sum of a student's three scores is 224. If the first is 13 points more than the second, and the sum of the first two is 29 more than twice the third, then what was the first score?
A) 65
B) 86
C) 52
D) 73

Question

Quizplus · Accepted Answer

The first score is 13 points more than the second, so the second score is x and the first score is x + 13. The sum of the first two scores is 29 more than twice the third, so x + (x + 13) = 2 * y + 29, where y is the third score. Simplifying this equation, we get 2x + 13 = 2y + 29. Subtracting 2y from both sides, we get 2x - 2y = 16. Dividing both sides by 2, we get x - y = 8. Adding y to both sides, we get x = 8 + y. Substituting this into the equation x + (x + 13) = 2 * y + 29, we get (8 + y) + (8 + y + 13) = 2 * y + 29. Simplifying this equation, we get 16 + 2y + 13 = 2 * y + 29. Subtracting 2y from both sides, we get 16 + 13 = 29. Subtracting 16 from both sides, we get 29 = 29. This equation is true, so the first score is 8 + y. Since the sum of the three scores is 224, we have 8 + y + y + y = 224. Simplifying this equation, we get 3y + 8 = 224. Subtracting 8 from both sides, we get 3y = 216. Dividing both sides by 3, we get y = 72. Substituting this into the equation x = 8 + y, we get x = 8 + 72 = 80. Therefore, the first score is 80.

The Sum of a Student's Three Scores Is 224