To find the total number of pages in the book after knowing Hank has read 150 pages, which represents 25 percent of the total pages, we can set up the equation as follows:
Let \( x \) be the total number of pages in the book. Since 25 percent of \( x \) is equal to 150 pages, we can write the equation:
\[ 0.25x = 150 \]
To find \( x \), we can multiply both sides of the equation by 4:
\[ x = 150 \times 4 \] \[ x = 600 \]
Now, looking at the options provided, there is an attempt at showing relationships through fractions. Evaluating these:
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\( \frac{25 \times 6}{100 \times 6} = \frac{150}{600} \) is a representation of the same relationship. This means if you scale both the numerator and denominator of the fraction \( \frac{25}{100} \) by 6, you get \( \frac{150}{600} \), which maintains the same ratio.
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\( \frac{100 \times 4}{25 \times 4} = \frac{400}{100} \) simplifies to equal 4, which is irrelevant to finding the total number of pages.
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\( \frac{25}{150} \) shows the ratio of what was read to what he read, but is not directly usable to find the total.
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\( \frac{150}{2} \div \frac{100}{2} = \frac{75}{50} \) simplifies to 1.5, also not helpful in this context.
Among these, the first option \( \frac{25 \times 6}{100 \times 6} = \frac{150}{600} \) accurately represents the relationship needed to express 25% of the total pages being 150 pages.
Thus, the best answer is: \[ \text{StartFraction } 25 \times 6 \text{ Over } 100 \times 6 \text{ EndFraction = StartFraction } 150 \text{ Over } 600 \text{ EndFraction} \]
3 answers