Problem 25 - Prealgebra

Question

Model Trains The size of a model train relative to an actual train is referred to as its scale. Each scale is associated with a ratio as shown in the table. For example, an HO model train has a ratio of 1 to 87, meaning it is \(\frac{1}{87}\) as large as an actual train. Elections During a recent election, 47 of every 100 registered voters in a certain city voted. If there were \(127,900\) registered voters in that city, how many people voted?

Step-by-Step Solution

Answer

60,113 people voted.

Step 1: Determine the Given Ratio and Apply It

The problem states that 47 of every 100 registered voters voted. This gives us a ratio of \( \frac{47}{100} \). To find out how many of the \( 127,900 \) registered voters this corresponds to, multiply the total number of voters by this ratio.

Step 2: Calculate the Number of Voters Who Voted

Multiply the total number of registered voters, \( 127,900 \), by the ratio \( \frac{47}{100} \). Calculate as follows:\[127,900 \times \frac{47}{100} \]This simplifies to:\[= 127,900 \times 0.47 = 60,113\]Hence, 60,113 people voted.

Key Concepts

Understanding Model Train Scale

Model train enthusiasts often discuss the 'scale' of their trains, which is a fascinating concept rooted in ratios. The scale represents the size relationship between a model train and its life-sized counterpart. These ratios are usually expressed in a simple form, such as 1 to 87. In this case, the number '1' refers to the model, while '87' refers to the real train's dimensions. This means that the model train is \(\frac{1}{87}\) of the actual train size.

Here's a simple guide on how to understand model train scales:

• The ratio tells you how much smaller the model is compared to the real train.
• Common scales include HO (1:87), N (1:160), and O (1:45).
• To convert any dimension of the real train into the model scale, divide the real size by the scale ratio. For example, if a real train car is 30 meters long, the HO scale model would be 30 / 87 meters long.

Understanding these key points about model train scales can help you choose the right size for your models and ensure they fit with the scenery and tracks you wish to create.

Calculating Voter Turnout

Voter turnout is a common statistic used to indicate civic participation in elections. In simple terms, it measures the percentage of eligible voters who cast a vote in an election. To calculate voter turnout, you use a ratio approach, which simplifies the process significantly.

In our scenario, we're told that 47 out of every 100 registered voters in a city went out to vote. This ratio, \(\frac{47}{100}\), illustrates what proportion of registered voters participated. To determine how many people that implies in a city with a larger population of registered voters, follow these steps:

• Convert the percentage, 47%, into a decimal: 0.47.
• Multiply the total number of registered voters by this decimal: \[127,900 \times 0.47 = 60,113\]
• This result, 60,113, represents the number of voters who actually participated in the election.

By using this straightforward calculation, it's possible to quickly gauge the level of voter engagement across different cities or regions.

Fraction Multiplication Made Easy

Multiplying fractions might seem tricky at first, but it’s very straightforward once you understand the basic rule: multiply the numerators together, then multiply the denominators together.

• Take two fractions you want to multiply, say \(\frac{3}{4}\) and \(\frac{2}{5}\).
• Multiply the numerators: 3 and 2 to get 6.
• Then multiply the denominators: 4 and 5 to get 20.
• Your product is \(\frac{6}{20}\).

Finally, simplify the fraction if possible. For \(\frac{6}{20}\), both 6 and 20 can be divided by 2, which gives you \(\frac{3}{10}\).

Fraction multiplication is often used in various real-world applications, such as calculating ratios in recipes, determining portions, and even in scaling models like trains. When you practice multiplying fractions, you’ll find it becomes second nature over time.