This question's explanation and your answers so far.
A社では，次の条件で eラーニングと集合教育の費用比較を行っている。年間の eラーニングの費用が集合教育の費用と等しくなるときの年間の受講者は何人か。ここで，受講者のキャンセルなど，記載されている条件以外は考慮しないものとする。 〔eラーニングの条件〕 ・費用は年間 60 万円の固定費と受講者 1 人当たり 2,000 円の運用費である。 〔集合教育の条件〕 ・費用は会場費及び講師代として 1 回当たり 25 万円である。 ・1 回当たり 50 人が受講し，受講者が 50 人に満たない場合は開催しない。
At 100 trainees, e-learning is 600,000 + 2,000 × 100 = 800,000 yen and classroom training is 5,000 × 100 = 500,000 yen, so the costs are not equal. In this range the e-learning option, weighed down by its fixed cost, is more expensive and has not yet reached the break-even point.
At 150 trainees, e-learning is 600,000 + 2,000 × 150 = 900,000 yen and classroom training is 5,000 × 150 = 750,000 yen, which are not equal. There is still a difference of 150,000 yen, so it has not reached the 200 trainees at which the two become equal.
正解 Let the number of trainees be x, express the annual cost of each method as a formula in x, and find the x at which they are equal. The annual e-learning cost is the fixed cost of 600,000 yen plus 2,000 yen per trainee, that is 600,000 + 2,000x yen. Classroom training costs 250,000 yen per session with 50 trainees per session, so the cost per person is 250,000 ÷ 50 = 5,000 yen, which becomes 5,000x yen for x trainees. Setting the two equal gives 600,000 + 2,000x = 5,000x, so 600,000 = 3,000x and x = 200. Therefore the costs of the two methods match when there are 200 trainees per year. Checking: e-learning = 600,000 + 2,000 × 200 = 1,000,000 yen and classroom training = 5,000 × 200 = 1,000,000 yen, which agree. Hence the correct answer is choice ウ, 200 trainees.
At 250 trainees, e-learning is 600,000 + 2,000 × 250 = 1,100,000 yen and classroom training is 5,000 × 250 = 1,250,000 yen, which are not equal. Beyond 200 trainees it is classroom training that becomes the more expensive option, so the size relationship is reversed.