You have an aquarium for your new pet, “Shamu” the killer whale, that contains 100,000 pounds of ocean water with a salinity of 30 o/oo.
a. Calculate how many pounds of salt are currently in the aquarium.
b. You think Shamu may be allergic to salt, so you decide to decrease the salinity from 30 o/oo to 10 o/oo. Calculate below how much water you need to add to the aquarium.
c. After you added the water in step b., you find out you were wrong and must return the salinity to 30 o/oo by adding more salt. Calculate how much salt (total) you now need.
I need to know how to do the problems.
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To solve these problems, we'll need to use mathematical formulas and conversion factors. Let's break down each question and go through the steps to find the answers.
a. Calculate how many pounds of salt are currently in the aquarium.
To find the amount of salt in the aquarium, we need to multiply the weight of the ocean water by the salinity, which is given as a percentage or parts per thousand (o/oo).
The formula we can use here is:
Amount of salt = weight of water * salinity
In this case, the weight of the water is given as 100,000 pounds, and the salinity is given as 30 o/oo.
So, to find the amount of salt in the aquarium:
Amount of salt = 100,000 * (30/1000)
To calculate this, we divide 30 by 1000 (to convert it to a decimal) and then multiply it by 100,000.
b. Calculate how much water you need to add to the aquarium to decrease the salinity.
To decrease the salinity from 30 o/oo to 10 o/oo, we need to calculate the weight of the additional water that needs to be added.
The formula we can use here is:
Weight of water to add = (amount of salt) / (final salinity - initial salinity)
In this case, the initial salinity is 30 o/oo, and the final salinity is 10 o/oo.
So, to find the weight of water to add:
Weight of water to add = (amount of salt) / (10/1000 - 30/1000)
We use the amount of salt obtained from question a. In addition, we divide the differences of salinities by 1000 to convert them to decimals.
c. Calculate how much salt (total) you now need to add to return the salinity to 30 o/oo.
To return the salinity to 30 o/oo, we need to calculate the total weight of the salt needed.
The formula we can use here is:
Total amount of salt needed = (weight of water + weight of water to add) * final salinity
In this case, the weight of water is 100,000 pounds, and the weight of water to add is obtained from question b. The final salinity is 30 o/oo.
So, to find the total amount of salt needed:
Total amount of salt needed = (100,000 + weight of water to add) * (30/1000)
By substituting the values, we can calculate the final result.
Please note that o/oo indicates parts per thousand, which means that for every thousand parts of water, there are o parts of salt.