PUC raised money for the recent disaster victims.They decided to allocate the money in manner: 1/3 of the money goes for medical supplies, 1/4 of what was left brought tents,2/3 of the remaining went to water purification systems, the rest of the money was spent on shipping costs. If $400was allocated for water purification systems, How much money was allocated on each of the other categories? How much money did PUC raise for this cause?

Question

PUC raised money for the recent disaster victims.They decided to allocate the money in manner: 1/3 of the money goes for medical supplies, 1/4 of what was left brought tents,2/3 of the remaining went to water purification systems, the rest of the money was spent on shipping costs. If $400was allocated for water purification systems, How much money was allocated on each of the other categories? How much money did PUC raise for this cause?

Answer 1

400 = 2/3 (2x/3 - 1/4 * 2x/3)

600 = 2/3 (x - 1/4x)
900 = x - x/4
900 = 3/4x
x = (4 * 900)/3
x = 1200

Answer 2

To find out how much money was allocated for each category, we need to work backward from the final amount spent on water purification systems.

Let's start by representing the total amount of money raised as "x".

1/3 of the money was allocated for medical supplies. This means that (1/3) * x was spent on medical supplies.

After deducting that amount, we are left with (2/3) * x to allocate towards other categories.

From this remaining amount, 1/4 was used to buy tents. So, (1/4) * (2/3) * x was used for tents.

After deducting that amount, we have (2/3) * x - (1/4) * (2/3) * x remaining.

We are told that $400 was allocated for water purification systems, which means (2/3) * x - (1/4) * (2/3) * x = $400.

Now, let's solve this equation to find the value of x:

(2/3) * x - (1/4) * (2/3) * x = $400

Simplifying the equation:
(2/3) * x - (1/6) * x = $400
(4/6) * x - (1/6) * x = $400
(3/6) * x = $400
(1/2) * x = $400

Now, we can solve for x:
x = ($400) / (1/2)
x = $800

So, PUC raised $800 for this cause.

Now, let's calculate the amount allocated for each category:

1. Medical supplies: (1/3) * $800 = $266.67 (rounded to two decimal places)

2. Tents: (1/4) * (2/3) * $800 = $133.33 (rounded to two decimal places)

3. Water purification systems: $400 (as given)

4. Shipping costs: Remaining amount after deducting the allocations for the other categories:
$800 - $266.67 - $133.33 - $400 = $0 (since there is no remaining amount)

Therefore, the allocation amounts for each category are:
- Medical supplies: $266.67
- Tents: $133.33
- Water purification systems: $400

And PUC raised $800 for this cause.