Percents: Percent Translation
Thirty percent of forty percent of fifty is sixty percent of what percent of two hundred?
Incorrect.
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You must have missed a zero somewhere along the way.
Incorrect.
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You must have missed a zero somewhere along the way.
**Solve the resulting equation**:
The 50 on the left side cancels with the factors of 10 and 5 in the denominator. That results in:
> $$\displaystyle \frac{3}{10}\cdot\frac{2}{5}\cdot50 = \frac{3}{5}\cdot 2x$$
> $$\displaystyle 6 = \frac{6x}{5}$$
Multiplying by 5 and dividing by 6 gives $$5 = x$$. That is, of course 5%.
Incorrect.
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Your equation should look like this:
$$\displaystyle\frac{30}{100}\cdot\frac{40}{100}\cdot 50 = \frac{60}{100}\cdot\frac{x}{100}
\cdot 200$$
The rest is reducing and combining fractions.
Incorrect.
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You must have missed a zero somewhere along the way.
Correct.
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Translate:
Use the percent language to translate the question, "Thirty percent of forty percent of fifty is sixty percent of what percent of two hundred".
> $$\displaystyle 30\% \mbox{ of } 40\% \mbox{ of } 50 = 60\% \mbox{ of } x\% \mbox{ of }200$$
> $$\displaystyle\frac{30}{100}\cdot\frac{40}{100}\cdot 50 = \frac{60}{100}\cdot\frac{x}{100} \cdot 200$$
Reduce the fractions:
When you reduce the fraction, you get $$\frac{30}{100} = \frac{3}{10}$$, $$\frac{40}{100} = \frac{2}{5}$$, $$\frac{60}{100} = \frac{3}{5}$$. On the right side, the 200 reduces with the 100 in the denominator to give 2.
> $$\displaystyle \frac{3}{10}\cdot\frac{2}{5}\cdot50 = \frac{3}{5}\cdot 2x$$
0.5%
1%
5%
50%
500%
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