Final answer:
To determine how many boys can earn N4,200 in 21 days, we use proportional reasoning to find that the same number of boys, 12, are needed as earned N2,400 in 5 days.
Step-by-step explanation:
The question involves proportional reasoning, which is a mathematical concept. To solve this problem, we need to determine how many boys would be needed to earn a different amount of money over a different period of time. First, we calculate the amount earned per day by one boy, which is N2,400 divided by 12 boys, giving us N200 per day per boy. Over 5 days, this is N1,000 per boy. The rate of earning will remain the same in any time-frame, so next we can calculate how much one boy would earn in 21 days, which would be N4,200. Once we have the daily earning rate, we can calculate the number of boys required to earn N4,200 over 21 days by setting up a proportion:
N1,000 over 5 days is to 12 boys as N4,200 over 21 days is to X boys.
From the proportion (12 boys * 5 days) / N1,000 = (X boys * 21 days) / N4,200, we can solve for X to find the number of boys needed. Simplifying the equation gives us 12 * 5 * N4,200 = N1,000 * 21 * X, and solving for X gives us X = (12 * 5 * N4,200) / (N1,000 * 21). This simplifies to X = 12, which means 12 boys are needed to earn N4,200 in 21 days.