SOLUTION: Hi In a castle there is enough food for 72 soldiers to last 24 days. After 4 days another 8 soldiers join them. How many days will the remaining food last. Thanks

Question 1184253: Hi
In a castle there is enough food for 72 soldiers to last 24 days. After 4 days another 8 soldiers join them. How many days will the remaining food last.
Thanks

Found 2 solutions by Theo, greenestamps:
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
you start with 72 soldiers.
number of soldiers * rate that each soldier eats * time = quantity.
formula becomes 72 * rate * 24 = 1
72 is the number of soldiers.
rate is the rate that each soldier eats at
24 is the number of days
1 is the quantity of food available when they start.

solve for rate to get rate = 1/(24*72) = 1/1728.
this means 1 soldier eats 1/1728 of the quantity of food each day.

8 more soldiers join them after 4 days.

in 4 days, 72 soldiers eat 72 * 4 * 1/1728 = 288/1728 of the quantity of food available.
this leaves (1728 - 288) / 1728 = 1440 / 1728 of the quantity of food left.

the number of soldiers is now 72 + 8 = 80.
the rate that each soldier eats remains the same.
the formula becomes:
80 * 1/1728 * time = 1440/1728.
this becomes 80/1728 * time = 1440/1728.
solve for time to get:
time = 1440/1728 * 1728/80 = 18 days.
the remaining quantity of food will last another 18 days.
the total amount of days the food will last is 4 + 18 = 22 days.

Answer by greenestamps(13195) (Show Source): You can put this solution on YOUR website!

Initially there is enough food for 72 soldiers for 24 days.

After 4 days, there is enough food for those 72 soldiers for 20 days.

When 8 more soldiers join them, the number of soldiers increases by a factor of 80/72 = 10/9.

That means the number of days the remaining food will last DECREASES by a factor of 10/9: 20*(9/10) = 18.

ANSWER: The remaining food will last 18 days.

Another solution method....

Initially, the number of "soldier-days" the food will last is 72*24=1728.

In 4 days, the amount of food consumed by the 72 soldiers is 72*4=288; the number of soldier-days of food remaining is 1728-288=1440.

The number of days 1440 soldier-days of food will last with 72+8=80 soldiers is 1440/80=18.

ANSWER: 18 days

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