When is it necessary to change a percent to a decimal in a w

[Divine]

It seems that in some word problems, it's not necessary to change a percent to decimal, but in others it is. Below are some examples of what I mean.

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Here is a word problem where percent to decimal is necessary to solve the word problem algebraically:

Earnings - In thousands:
Some college: 47
High school diploma: unknown

The annual salary for men with some college is an increase of 20.5% over the annual salary for men whose highest educational attainment is a high school diploma. What is the annual salary, to the nearest thousand dollars, for men whose highest educational attainment is a high school degree?

x + .205x = 47 (Formula setup - Notice that I turned the percent to a decimal)
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here is a word problem where percent to decimal is not necessary to solve the word problem algebraically:

In 2005, 19.4% of people in the US spoke a language other than English at home. For the period between 00-05, this had been increasing by approximately .4% per year. If this trend continues, by which year will 23% of people in the US speak a language other than English at home?

19.4 + .4x = 23 (Formula setup - Notice that I didn't need to change any of the original information)
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In the last example, I would have changed all of the percents in the question to decimals, but the formula on my answer page shows that it's not necessary to change it at all.

When is it necessary to change a percent to a decimal in a word problem? Any tips?

[stapel_eliz]

In the second instance, you're not trying to find the percentage of anything; instead, you're actually working with the percentage points. That is, in the second example, the "percent" is actually the numerical value of the thing you're working with, like "gallons" or "dollars".

You switch percentages from "%" form to decimals when you're finding the percentage of something else. When you're just working with percentage points as their own quantities, you can switch or not, but the answer will be the same.

In 2005, 19.4% of people in the US spoke a language other than English at home. For the period between 00-05, this had been increasing by approximately .4% per year. If this trend continues, by which year will 23% of people in the US speak a language other than English at home?

0.194 + 0.004x = 0.23
0.004x = 0.036
x = 0.036/0.004 = 9