Two Club Budget Requests
The student council has 50,000 yen to divide between two clubs. The robotics club asks for 32,000 yen. Its written request says: “We need 32,000 yen for motors and sensors. Last year we received 20,000 yen and spent 18,500 yen. We have 6 members.” The art club asks for 30,000 yen. Its request says: “We need 30,000 yen for clay and printing. Last year we received 15,000 yen and spent all of it. We have 14 members.” A council member says, “The robotics club has a larger shortfall, so it should get more.” Another says, “The art club has more members, so it should get more.” The council also has a rule: no club may receive more than 60% of the total budget. The robotics club's adviser has offered to cover 5,000 yen of the robotics request if the council funds the rest.
1. What is the maximum amount the council can give to one club under its rule?
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Maximum: 30,000 yen.
Reasoning: 60% of 50,000 yen is 0.60 × 50,000 = 30,000 yen. The rule says “no more than 60%,” so 30,000 is allowed but 30,001 is not. This means the robotics club's 32,000-yen request cannot be fully funded by the council; the art club's 30,000-yen request is exactly at the cap. The calculation is simple, but the judgement is noticing that the rule constrains the robotics request before any fairness debate begins.
2. The first council member says robotics has a larger shortfall. Is that supported?
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Not clearly supported. “Shortfall” is undefined in the passage, and the answer changes depending on the definition.
Reasoning: If shortfall means “request minus last year's funding,” robotics is 32,000 − 20,000 = 12,000, while art is 30,000 − 15,000 = 15,000. On that measure, art has the larger shortfall. If shortfall means “raw request size,” robotics is larger by 2,000 yen, but that is not a need gap. The council member may be comparing the headline request numbers without checking the previous year. A careful reader should ask for a definition before accepting the claim.
3. How does the adviser's offer change the decision?
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Effect: If the adviser covers 5,000 yen, the council needs to fund only 27,000 yen of the robotics request. That is under the 30,000-yen cap and leaves 23,000 yen for the art club if the full 50,000 yen is allocated.
Reasoning: The offer reduces the robotics burden but does not make the decision automatic. The council still has to decide whether 27,000 to robotics and 23,000 to art is fair, given that art requested 30,000. The key point is that the adviser's offer changes the arithmetic and creates room for a compromise; it does not by itself prove which club deserves more.