Confusing arithmetic math help.

Question

A garrison of 500 men had provisions for 27 days. After 3 days a reinforcement of 300 men arrived. For how many more days will the remaining food last?

Answer 1

After 3 days, they had enough food for 500 men for 24 days.

Assume the men ate ONE meal per day.

So, that's 500 * 24 = 12000 meals.

The extra 300 men makes a total of 800 men.

The 12000 meals divided among all 800 men is:

12000/800 = 15 meals

So, there would be enough for the 800 men to have 15 meals

At one meal per day, that's 15 days.

After 3 days, and without the extra men,

they originally had enough food for 24 more days.

But, with all 800 men, they have enough for only 15 days.

The remaining food will last for 15 days.

Answer 2

Hello Krugen,

So there are two ways to do this. The first way uses ratios. If there is enough food left for 500 people for 24 days, since 3 days have passed, then we must calculate how much would be left for 800 people.

500 people = 24 days

800 people = ? days

The number of people increased by 1.6 (500*1.6=800), therefore the amount of days the food will last must decrease by this same amount, 24/1.6= 15. Therefore there is enough food for 15 days.

The other way to do this would be to have an arbitrary amount of food and calculate the number of days that way. For instance, if we assume that each person gets 1 meal each day then:

500 * 27= 13,500 total meals

After 3 days, we will have 12,000 meals left (13,500- (500*3) = 12,000)

However, we also have 300 more people. So, 12,000/800= 15 meaning that the remaining amount of provisions will last 15 days.

I hope this helps!