The swimming pool water calcium level is 300 parts per million.
It needs to be 200 parts per million.
The replacement water has a calcium level of 100 parts per million.
What percent of the old water needs to be replaced?
Please show the formula.
There is no single
formula that solves all word problems similar to this one. You are probably expected to (1) pick a symbol to represent what they're asking for, (2) consider this unknown quantity
along with the given values and scenario until you realize relationship(s) between them, and then (3) use your symbol to write and solve an equation.
In case you're wondering, parts per million (
ppm) is a ratio without units, just like
percent is a ratio without units.
1
% is 1/100th of the whole
1
ppm is 1/1000000th of the whole
A nice thing about this exercise is that none of the volumes matter because everything is proportional. For example, any water removed is 300ppm -- whether you remove 1,000 liters or you remove one drop. The swimming pool could be olympic-sized (2.5 million liters) or backyard wading-size (100 liters) -- the answer will be the same. So focus on the parts in the original water and the parts in the replacement water, and resist the urge to think of volumes.
Here's a quasi-math description of
what's happening.
Some percent of 300 parts is removed from the 300 parts, and then
the same percent of 100 parts is added. The result is 200 parts.
Can you pick a symbol to represent this unknown percent and use it to write an equation that models
what's happening?
Please show us what you tried, and we can go from there. :cool:
Also, kindly read
the forum guidelines. Thank you!