# Percent Problems

- - Pre-Algebra

The word percent came from the Latin word “per centum” which means every hundred or fraction of a hundred. Percentage is the result when taking a certain percent of a number. For instance, you are asked to find 20% of 50. This means if 50 is divided into 100 equal parts and you take 20 parts of those, what is the result?

To answer this, we have $50 \div 100=\frac{1}{2}$ then you multiply it by 20, since we are taking 20 parts, then we arrive at $20 \left (0.5 \right )=10$. Therefore, 20% of 50 is equal to 10. Similarly, it can be viewed in this way, 20% refers to the 20 parts out of 100. So we can express 20 as a fractional part of 100, then $\frac{20}{100} \left (50\right )=\frac{1000}{100}=10$. As previously learned 20% can be written into 0.20 in decimal form. Likewise, 20% of $50 = 0.20 \left(50 \right) = 10$. From these illustrations, we can summarize the procedures on how to find percentage.

Based from the illustration presented above with the use of the definition of percent, we can be able to formulate some equivalent rule in finding the percent of a number.

To find a certain percent of a given quantity:

Method 1: Write the percent as a fraction out of 100 and omit the percent sign (%). Change “of” to a multiplication sign. Multiply the fraction by the given quantity.

Examples:

1. What is 10% of 50?
2. 25% of 120 is what number?
3. What is 5% of 1000?
4. Karen saved P5.00 by purchasing a set of pens than purchasing then individually. If P5.00 is 8% of the price for one set, what is the price of one set of pens?

Solutions:

1. Since $10 \% = \frac{10}{100}$, then $\frac{10}{100} \left(50\right)=\frac{500}{100}=5$.
2. Since $25\%=\frac{25}{100}$, then $\frac{25}{100} \left(120\right)=\frac{3000}{100}=30$.
3. Since$5\%=\frac{5}{100}$, then $\frac{5}{100} \left(1000\right)=\frac{5000}{100}=50$.
4. When the percent statement is translated mathematically, it would be: $5 = 8\%n$, where $n$ is the price for one set of pens. Since 8% is equivalent to $\frac{8}{100}$, then the equation can also be written as $5=\frac{8n}{100}$. Multiplying both sides by the reciprocal of $\frac{8}{100}$ (multiplication property), then $5\frac{100}{8}=n$, where $n=\frac{500}{8}=62.5$.

$\therefore$, the price for 1 set of pens is P62.5.

Method 2: Convert the given percent into its equivalent decimal number by following conversion rule then multiply it to the given quantity.

Examples:

1. What is 10% of 50?
2. 25% of 120 is what number?
3. What is 5% of 1000?
4. Karen saved P5.00 by purchasing a set of pens than purchasing then individually. If P5.00 is 8% of the price for one set, what is the price of one set of pens?

1. $10\% = 0.10$
$10\% \left(50\right) = 0.10 \left(50\right) = 5$
2. $25\% = 0.25$
$25\%$ of $120 = 0.25 \left(120\right) = 30$
3. $5\% = 0.05$
$5\% \left(1000\right) = 0.05\left(1000\right)=50$
4. When the percent statement is translated mathematically, it would be: $5 = 8\%$ , where is the price for one set of pens. Convert 8% into 0.08, then $5 = 0.08n$. Since $n$ is a factor, divide both sides by 0.08.

$\begin{array}{c@{\,}c@{\,}c@{\,}c@{\,}c@{\,}c@{\,}c@{\,}c@{\,}c@{\,}c@{\,}c} &\displaystyle \frac{5}{0.08}&=&n \\ &n&=&62.5 \\ \end{array}$

$\therefore$, the price for 1 set of pens is P62.5.
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