Problem 68
Question
For exercises \(67-82\), use the five steps and a proportion. Find the number of adults used to create the ratio "four out of five." Four out of five adults now use the Internet. 184 million adults are online from their homes, offices, schools or other locations. (Source: www.harrisinteractive.com, Nov. 17, 2008)
Step-by-Step Solution
Verified Answer
230 million adults
1Step 1: Understand the problem
The exercise tells us that 'four out of five' adults use the Internet. This means for every 5 adults, 4 of them are using the Internet. We need to find the total number of adults if 184 million is 4 out of those 5.
2Step 2: Set up the proportion
We can set up a proportion to represent this situation. Let the total number of adults be denoted by x. The proportion will be \(\frac{4}{5} = \frac{184}{x}\)
3Step 3: Cross-multiply to solve for x
Cross-multiply the equation \( \frac{4}{5} = \frac{184}{x} \) to get 4x = 5 * 184.
4Step 4: Simplify the equation
Simplify the right-hand side to get 4x = 920.
5Step 5: Solve for x
To isolate x, divide both sides by 4: \( x = \frac{920}{4} \), which simplifies to x = 230.
Key Concepts
proportionscross-multiplicationsolving equationsratio problems
proportions
A proportion is an equation that states two ratios are equal. A ratio compares two quantities by division. For example, if we say 'four out of five' adults use the Internet, we can write this as the fraction \[ \frac{4}{5} \]. Now, if we need to find the total number of adults where 184 million is 'four out of five', we can set up a proportion equation. The initial ratio given, \[ \frac{4}{5} \], is set equal to another ratio where we know one part but need to find the total:
\[ \frac{4}{5} = \frac{184}{x} \]. Using proportions helps us find the unknown quantity, in this case, the total number of adults.
\[ \frac{4}{5} = \frac{184}{x} \]. Using proportions helps us find the unknown quantity, in this case, the total number of adults.
cross-multiplication
Cross-multiplication is a method used to solve proportions. When we have an equation of the form \[ \frac{a}{b} = \frac{c}{d} \], we can find the value of the unknown by cross-multiplying. This means multiplying the numerator of one fraction by the denominator of the other. For our proportion, \[ \frac{4}{5} = \frac{184}{x} \], we cross-multiply to get the equation:
\[ 4 \times x = 5 \times 184 \]. This simplifies to 4x = 920. Cross-multiplication transforms a proportion into a simple linear equation, making it easier to solve.
\[ 4 \times x = 5 \times 184 \]. This simplifies to 4x = 920. Cross-multiplication transforms a proportion into a simple linear equation, making it easier to solve.
solving equations
Solving equations is a critical skill in algebra. After we've set up our proportion and cross-multiplied to get the equation 4x = 920, the next step is to solve for x. To isolate x, divide both sides of the equation by 4:
\[ x = \frac{920}{4} \]. Performing the division, we get x = 230. This means, based on the proportion given, there are 230 million adults in total if 184 million is 'four out of five'. Solving equations involves isolating the variable on one side to find its value.
\[ x = \frac{920}{4} \]. Performing the division, we get x = 230. This means, based on the proportion given, there are 230 million adults in total if 184 million is 'four out of five'. Solving equations involves isolating the variable on one side to find its value.
ratio problems
Ratio problems often involve comparing parts to a whole or comparing two quantities. In our exercise, the ratio 'four out of five' compares the part (adults using the Internet) to the whole (total number of adults). To solve ratio problems:
- Identify the ratio.
- Set up a proportion.
- Use cross-multiplication.
- Solve the resulting equation. This process is useful for understanding relationships between quantities and making predictions. For example, if a study shows a ratio like 'four out of five', we can use this to find total amounts when given one part, such as '184 million adults using the Internet.'
- Identify the ratio.
- Set up a proportion.
- Use cross-multiplication.
- Solve the resulting equation. This process is useful for understanding relationships between quantities and making predictions. For example, if a study shows a ratio like 'four out of five', we can use this to find total amounts when given one part, such as '184 million adults using the Internet.'
Other exercises in this chapter
Problem 67
For exercises 39-82, simplify. $$ \frac{p^{2}-64}{p+4} \div \frac{p+8}{-p-4} $$
View solution Problem 67
$$ \text { For exercises 67-72, simplify. } $$ $$ \frac{x^{3}+8}{x^{2}-4} $$
View solution Problem 68
For exercises 39-82, simplify. $$ \frac{k^{2}-36}{k+3} \div \frac{k+6}{-k-3} $$
View solution Problem 68
$$ \text { For exercises 67-72, simplify. } $$ $$ \frac{x^{3}+27}{x^{2}-9} $$
View solution