Algebra and Up:
Question: Four teams have just finished a year-long competition. The Serpents scored 32 points more than 1.25 times the number of points scored by the Badgers. The Badgers scored 3 less than 5/6 the number of points scored by the Eagles. The Serpents, Eagles, and Badgers scored a total of 1,250 points between the three of them. The Lions won the competition by 10 points. How many points did the Lions score?
Answer: 482 points
Solution: First, we set up a system of equations for the points scored by the Serpents,
the Badgers, and the Eagles:
S = 1.25B + 32
B = 5/6E – 3
S + B + E = 1,250
When we solve this system, we get S = 472, B = 352, and E = 426. Since S is the greatest value so far and we know that the Lions beat that score by 10 points, the Lions must have scored 472 + 10 = 482 points.
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