Problem 33 - Elementary Algebra

Question

Find the percent of vehicles belonging to residents that can be parked in legal curb spaces. Round to the nearest percent. The need for extra parking is clear: There are about 850 legal curb spaces in UCLA's North Village, but about 5,700 vehicles belonging to residents. (Source: www.latimes.com, June 28, 2011)

Step-by-Step Solution

Answer

15%

Step 1: Understand the Problem

We need to find what percent of 5,700 vehicles can be parked in 850 legal curb spaces at UCLA's North Village.

Step 2: Set Up the Percent Formula

Use the formula \(\text{Percent} = \frac{\text{Part}}{\text{Whole}} \times 100\). In this exercise, the 'Part' is the number of legal curb spaces (850), and the 'Whole' is the number of vehicles (5,700).

Step 3: Substitute the Values

Substitute the values into the formula: \(\text{Percent} = \frac{850}{5700} \times 100\).

Step 4: Simplify the Fraction

Simplify the fraction \(\frac{850}{5700}\) to get a decimal value. \(\frac{850}{5700} \approx 0.149\).

Step 5: Convert Decimal to Percentage

Multiply the decimal by 100 to get the percentage: \(0.149 \times 100 = 14.9\).

Step 6: Round to the Nearest Percent

Round 14.9 to the nearest whole number. 14.9 rounds to 15.

Key Concepts

percent formula

Understanding how to find a percent is crucial in many situations. The percent formula helps you determine what portion of a whole something represents in terms of percentage. The formula to remember is: \[ \text{Percent} = \frac{\text{Part}}{\text{Whole}} \times 100 \] Here, 'Part' refers to a subset we are focusing on, while 'Whole' is the total set. For example, if we are asked to find what percent of 5,700 vehicles can park legally in 850 spots, the 'Part' is 850 and the 'Whole' is 5,700. By substituting these values into our formula, we get: \[ \text{Percent} = \frac{850}{5700} \times 100 \] This formula helps convert a fraction into a percentage, making it easier to understand the ratio.

simplifying fractions

Simplifying fractions is an important skill in both math and everyday situations. When we simplify a fraction, we are making it easier to understand by reducing it to its simplest form. Suppose we have the fraction \( \frac{850}{5700} \). To simplify, we divide the numerator and denominator by their greatest common divisor (GCD). Sometimes, it’s not obvious, and we might need to use a calculator. Simplifying helps to see the fraction in its simplest form which is useful for further calculation.For simplifying our example, suppose you couldn't find the GCD right away. Using a calculator or a step-by-step method dividing until the simplest form is achieved.Ultimately, for our exercise: \[ \frac{850}{5700} \rightarrow 0.149 \] This decimal will be important in the following steps.

converting decimals to percentages

Languages of fractions, decimals, and percentages often overlap and understanding conversions is key. When we have a decimal such as 0.149, we often need to convert it to a percentage to make a clearer interpretation. Conversion is straightforward: simply multiply the decimal by 100. For example: \[ 0.149 \times 100 = 14.9 \]. This step moves '0.149' from a small decimal to a more comprehensible percentage. Essentially, multiplying by 100 shifts the decimal two places to the right. This gives a quick means to express the value in percentage, making it easier for comparing and understanding proportions.

rounding numbers

Rounding numbers makes them simpler to work with, especially in percentages where whole numbers are preferred for practicality. To round a number to the nearest percent, we follow some general rules:

• Identify the rounding digit (which is the digit in the desired place value, here it's the tenths place for percentages).
• Check the digit immediately right to it.
• If this digit is 5 or greater, round up the rounding digit by one.
• If it is less than 5, retain the rounding digit.

For example, to round 14.9: Look at '9' in the tenths place. Since 9 is greater than 5, we round up 14.9 to 15. Hence, 14.9 percent becomes 15 percent.So, about 15% of 5,700 vehicles can be legally parked within the 850 available spaces.