FILE No.177Unsolved
The results of a math test (100 points maximum) were handed back. Student A scored twice Student B's score, Student C scored 10 points higher than B, and Student D scored 20 points lower than A. The average of the four is 50 points.
What is Student A's score?
If you get stuck, open the hints one at a time, in order.
Let B's score be □ and write all four scores as expressions.
If the average of four is 50, what is the total?
Once you know □, A is twice that.
What is Student A's score?
Choose the answer closest to the truth.
70 points
The answer is "70 points."
Let B's score be □. Then A = 2□, C = □ + 10, D = 2□ − 20. The total of the four is 2□ + □ + (□ + 10) + (2□ − 20) = 6□ − 10. The average is 50, so the total is 200. 6□ = 210, □ = 35. A = 70 points.
Because you try to think about all four scores at once and get confused.
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