SOLUTION: 1500 students have enough food for 24 days. If 500 other students joined and 20% food is also reduced to every student. How much longer will the food last?

Question 1014930: 1500 students have enough food for 24 days. If 500 other students joined and 20% food is also reduced to every student. How much longer will the food last?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
500 students have enough food for 24 days.

let s = number of students.
let d = the number of days.
let m = amount of food available to each student each day.
let f = total amount of food available.

a general formula would be:

f = s * m * d

this formula says that the total amount of food available is equal to the number of students times the amount of food available to each student each day times the number of days.

when you have 1500 students and have enough food for 24 days, the formula becomes:

f = 1500 * m * 24.

if you add 500 students and reduce the food available to each student by 20%, the formula becomes:

f = 2000 * (m - .2 * m) * d

you can simplify this equation to get f = 2000 * .8 * m * d

you can simplify this equation further to get f = 1600 * m * d

you have 2 equations that need to be solved simultaneously.

they are:

f = 1500 * m * 24.
f = 1600 * m * d

since f = 1500 * m * 24, you can replace f in the second equation by its equivalent value to get:

1500 * m * 24 = 1600 * m * d

if you divide both sides of this equation by m, you will get:

1500 * 24 = 1600 * d

if you divide both sides of this equation by 1600, you will get:

(1500 * 24) / 1600 = d

solve for d to get d = 22.5

this says that, if you add 500 students and reduce the amount of food available to each student by 20%, the food will last for 22.5 days instead of 24 days.

to see if this makes sense, do the following:

assume that you originally had 180,000 pounds of food available in total.

that means that f = 180,000

when f = 180,000, your original equation of f = 1500 * m * 24 becomes 180,000 = 1500 * m * 24.

solve for m and you will get m = 5.

your equation becomes 180,000 = 1500 * 5 * 24

since 1500 * 5 * 24 = 180,000, the equation is true.

now, if you add 500 students, the number of students becomes 2000 instead of 1500.

if you reduce the amount of food available to each student by 20%, the amount of food available to each student becomes 4 instead of 5.

the number of days will change, so show it as d in the new equation until you can find out what the new value is.

the new equation is:

180,000 = 2000 * 4 * d

solve for d to get d = 22.5

this confirms the solution is correct.

the question is:

How much longer will the food last?

the answer is that the food will not last longer.

it will last 22.5 days instead of 24 days.

it will therefore last 1.5 days less.

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