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?
$X = Amt. raised.
X/3 = Amt. for med. supplies.
1/4(2x/3)=2x/12 = x/6 = Amt. for tents.
(2/3)(X-x/3-x/6) = (2/3)(X-3x/6) =
(2/3)(3x/6) = = 6x/18 = x/3 = Amt. for water purification.
x/3 = $400,
X = $1200 = Amt. raised.
x/3=1200 / 3 = $400 for med. supplies.
x/6 = 1200 / 6 = $200 for tents.
Bal = 1200 - 1000 = $200.
To find out how much money was allocated to each category, let's begin by assigning a variable to represent the total amount raised by PUC for the disaster victims.
Let's say the total amount raised is 'x' dollars.
According to the given information, 1/3 of the money goes to medical supplies. Therefore, the amount allocated to medical supplies is (1/3) * x dollars.
Now we have (2/3) of the money left. From this remaining amount, 1/4 is allocated to tents. Hence, the amount allocated to tents is (1/4) * (2/3) * x dollars.
Next, we have (3/4) * (2/3) * x dollars remaining. Of this amount, $400 is allocated to water purification systems. So, we can set up the equation:
(2/3) * (3/4) * x = $400
Simplifying this equation, we get:
(2/4) * x = $400
Multiplying both sides by 4/2, we find that x = $800.
Therefore, PUC raised $800 for this cause.
To determine how much money was allocated to each category, we can substitute this value back into the previous calculations:
1/3 of $800 goes to medical supplies: (1/3) * $800 = $266.67
1/4 of (2/3) * $800 goes to tents: (1/4) * (2/3) * $800 = $133.33
2/3 of (3/4) * (2/3) * $800 goes to water purification systems: (2/3) * (3/4) * (2/3) * $800 = $400
The rest of the money is spent on shipping costs, so we can calculate this by subtracting the amounts allocated for the other categories from the total raised:
Shipping costs = $800 - ($266.67 + $133.33 + $400) = $0
Therefore, no money is allocated to shipping costs.