A camp needs 900kg of food for 40 campers to last for 20 days. For how many days, will 540 kg of food last for 30 campers?

The food will last for 16 days

Step-by-step explanation:

Proportions

We need to know how the variables depend on each other.

It's clear that:

The more campers, the more food the camp needs.

The more time, the more food the camp needs.

Therefore, the amount of food (F) is directly proportional to the number of campers (c) and the time (t).

This can be written as:

F = k.c.t

Where k is a constant that we'll be found by knowing the camp needs F=900 Kg of food for c=40 campers and t=20 days:

900 = k*40*20=800k

Thus:

k=9/8

And:

F = 9/8 c.t

We now need to find how many days will F=540 kg of food will last for c=30 campers. So we solve the equation for t:

t = 8/9 * F/c

t = 8/9 * 540/30

t = 16 days

The food will last for 16 days

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240

step-by-step explanation: