Question 433642: a) A garrison has enough food to last for 24 days. How much longer will the food last if each individual ration can be reduced by 20 %?
b) By how much will each individual ration have to be reduced if the food is to last 40 days?
Answer by rwm(914)   (Show Source):
You can put this solution on YOUR website! Let F = the number of pounds in the total food supply.
The soldiers will use up the food in 24 days.
(a) Let x = amount of food (in pounds) each soldier eats per day.
In 24 days, they will eat 24x pounds of food, using up the F pounds of supply.
We have: 24x = F *
We reduce each soldier's ration by 20%,
then each soldier gets only 80% of his normal amount.
That is, each soldier eats 0.80x pounds of food per day.
And this will last N days.
We have: N(0.80x) = F **
Equate the two statements: N(0.80x) = 24x
Divide by x: 0.80x = 24
Divide by 0.80: x = 30
Therefore, the food will last 30 days, 6 days longer.
(b) We want the food to last 40 days.
Each soldier will get a fraction of what he usually gets.
Call that fraction r.
Each soldier gets rx pounds of food per day.
In 40 days, they will eat: 40rx pounds of food.
In part (a), the total amount of food is 24x.
So we have: 40rx = 24x r = 24/40 = 3/5 = 60%
Each soldier will get only 60% of his normal ration.
Therefore, each ration is reduced by 40%.
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