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Chapter 7: Problem 60

Solve the problem using a percent proportion. What is \(28 \%\) of \(70 ?\)

Short Answer

Expert verified
19.6

Step by step solution

01

- Understand the problem

The exercise asks for the value that corresponds to 28% of 70. This involves finding a part of a whole using percentage.
02

- Set up the proportion

The percent proportion equation is \ \( \frac{part}{whole} = \frac{percent}{100} \). Here, the 'part' is the unknown value, the 'whole' is 70, and the 'percent' is 28. Substitute these values into the equation: \ \( \frac{x}{70} = \frac{28}{100} \).
03

- Cross-multiply to solve for the unknown

To solve for the unknown value, cross-multiply by multiplying the numerator of one fraction by the denominator of the other and set the two products equal: \ \( x \cdot 100 = 28 \cdot 70 \).
04

- Simplify the equation

Multiply the numbers on the right side of the equation: \ \( x \cdot 100 = 1960 \).
05

- Solve for x

Isolate x by dividing both sides of the equation by 100: \ \( x = \frac{1960}{100} \). Simplify the fraction: \ \( x = 19.6 \).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

percentage
Understanding percentage is key to solving problems like the given exercise. A percentage is a way of expressing a number as a fraction of 100. It is denoted by the symbol \(%\). For example, 28% means 28 out of every 100 parts. So, when asked to find 28% of a number like 70, we are looking for how much 28% (or 28 out of 100) of 70 is.
part-whole relationship
The part-whole relationship helps to understand percentages better. In this context, 'part' refers to the portion of the whole that we are interested in calculating. 'Whole' is the total or complete amount we are considering. For instance, in our exercise, 70 is the whole amount and the part we are looking for is 28% of 70.
cross-multiplication
Cross-multiplication is a method used to solve proportions. A proportion is an equation that says two ratios are equal. Our percent proportion for the exercise is set up as \(\frac{x}{70} = \frac{28}{100}\). To solve this, we use cross-multiplication by multiplying the numerator of each fraction by the denominator of the other. This gives us \(x \cdot 100 = 28 \cdot 70\).
solving equations
After setting up and cross-multiplying the proportion, the final step is solving the equation. From the cross-multiplication step, we get \(x \cdot 100 = 1960\). To isolate x, divide both sides by 100: \(x = \frac{1960}{100}\). Simplifying this fraction, we find that \(x = 19.6\). Thus, 28% of 70 is 19.6.

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