how to do this?
In an island, a number of survivors have enough food to last for 5 days. After 2 days, 4 of the survivors died and the remaining food lasted for 5 more days. Find the original number of survivors...
If there are n survivors, there are 5n meals.
After 2 days, 2n meals have been eaten, leaving 3n
Then the 3n meals lasted the n-4 survivors 5 days:
3n/(n-4) = 5
Now just find n
n=10
How to find the n
To solve this problem, let's break it down step by step:
Step 1: Define the variables
Let's assume the original number of survivors is 'N', and the original amount of food that could last them 5 days is 'F'.
Step 2: Calculate the daily consumption rate
Since the survivors have enough food to last for 5 days, we can calculate the daily consumption rate as 'F/5'. This means that on average, they consume 'F/5' amount of food each day.
Step 3: Calculate the total amount of food consumed after 2 days
In 2 days, the survivors would have consumed '2 * (F/5)' amount of food.
Step 4: Calculate the remaining amount of food
After 2 days, 4 survivors died, so the remaining number of survivors would be 'N - 4'. Therefore, the remaining amount of food is equal to the original amount of food minus the amount consumed after 2 days: 'F - 2 * (F/5)'.
Step 5: Set up the equation
Since the remaining amount of food lasted for 5 more days, we can set up the equation: '5 * (F - 2 * (F/5)) = (N - 4) * F/5'.
Step 6: Simplify the equation
By simplifying the equation, we get: '5F - 2F = (N - 4)F/5'.
Step 7: Solve for N
Simplifying further, we get: '3F = (N - 4)F/5'. Dividing both sides by F, we have: '3 = (N - 4)/5'. Multiplying both sides by 5, we obtain: '15 = N - 4'. Finally, adding 4 to both sides, we get: 'N = 19'.
Therefore, the original number of survivors on the island was 19.