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.

Thanks.

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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.

Thanks.

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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 quantityThe 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.

In case you're wondering, parts per million (

1

1

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

Can you pick a symbol to represent this unknown percent and use it to write an equation that models

Please show us what you tried, and we can go from there. :cool:

Also, kindly read the forum guidelines. Thank you!

300 (- 300x + 100x) = 200

300 - 200x = 200

(300 - 300) - 200x = (200 - 300)

- 200x = - 100

(- 200x / -200) = (- 100 / - 200)

x = 0.5

x = 50%

([desired water ppm] - [old water ppm]) / ([water to be added ppm] - [old water ppm]) = decimal * 100 = percent to drain.

Any comments?

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Interesting. It's a simplified ratio of two different percent changes, where each percent change is from one ppm to another. And, because both percent change and ppm are ratios themselves, it's a ratio of ratios of ratios.([desired water ppm] - [old water ppm]) / ([water to be added ppm] - [old water ppm]) = decimal * 100 = percent to drain [and replace].

Any comments?

Looks like you have found a formula, for the particular mixture scenario taking place in this exercise.

Your algebraic solution also looks good.

([desired water ppm] - [old water ppm]) / ([water to be added ppm] - [old water ppm]) = decimal * 100 = percent to drain.

200-300/100-300

-100/-200

([old water ppm] - [desired water ppm]) / ([old water ppm] - [water to be added ppm]) = decimal * 100 = percent to drain.

300-200/300-100

100/200

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If you wanted to increase the calcium concentration, you could still use either.

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Hello, again. I had forgotten to mention a couple things about notation.300 - 300x + 100x = 200

300(-300x + 100x) = 200

300 - 200x = 200

(300 - 300) - 200x = (200 - 300)

- 200x = - 100

(- 200x / -200) = (- 100 /- 200)

When you typed grouping symbols around the like-terms on the left-hand side (in your first step above), you placed the subtraction operator inside the grouping symbols (shown in red).

I realize that you were thinking in terms of negative 300x, but you need to

300

Without this correction, your typing actually means that (-300x+100x) is being

Less important are some instances where you put space between a negative sign and its number.

I think -200 is better than

~ Cheers