JAMB 2022 Mathematics · Question 34

The cost C of running a school is directly proportional to the number of students N, if 20 students cost #10,000, How many students can #1,000,000 cover?

Options

A.3000
B.1000
C.2000
D.4000

Answer: C. 2000

Explanation written with AI and checked against the answer key

Analyze the question The cost C is directly proportional to the number of students N. We are told 20 students cost ₦10,000, and we need to find how many students ₦1,000,000 can cover. Concept Direct proportion means C = kN, where k is the constant of proportionality (the cost per student). Solution Step 1: Find k. 10,000 = k × 20 k = 10,000 ÷ 20 = 500 So each student costs ₦500. Step 2: Use k to find N when C = 1,000,000. 1,000,000 = 500 × N N = 1,000,000 ÷ 500 = 2000 Check: 2000 × 500 = 1,000,000 ✓ 2000. **Tip: In direct proportion questions, always find the constant k first, then substitute. You can also use a quick ratio shortcut: 1,000,000 ÷ 10,000 = 100, so the money is 100 times larger, meaning the number of students is 100 times larger: 20 × 100 = 2000.

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