Question

Translate to an equation and solve. What percent of 68 is \(17 ?\)

Short answer

Answer: Approximately 25%

Step-by-step solution

Set up the proportion with the unknown percentage

We can set up the proportion as: \(\frac{x}{100}=\frac{17}{68}\) where x is the unknown percentage.

Solve for x

To solve for x, we can cross-multiply: \(68x=17*100\) Now, divide both sides by 68: \(x=\frac{17*100}{68}\)

Calculate the percentage

Now, perform the calculation to find the percentage: \(x=\frac{1700}{68}\approx 25\) So, about 25% of 68 is 17.

Key concepts

Solving Equations

To solve equations, you need to find the value of the unknown in the equation that makes the equation true. In this scenario, the unknown was the percentage, which we represented with the variable \(x\). By translating the problem into a mathematical equation, we established that \(x\) percent of 68 equals 17. This essentially forms a basic equation:

• Start by representing the percentage you want to find as a variable (e.g., \(x\)).
• Translate the problem statement into an equation (e.g., \(\frac{x}{100} = \frac{17}{68}\)).
• This equation stated that \(x\), as a fraction of 100, equals \(\frac{17}{68}\).

The task was to solve for \(x\) to find its numerical value.

Proportions

A proportion is an equation that states that two ratios are equivalent. In this exercise, the proportion we set up compared the unknown percentage to the given numbers in the problem (68 and 17).

• Proportions are a powerful mathematical tool to solve problems involving ratios.
• We set up the proportion as \(\frac{x}{100} = \frac{17}{68}\), where \(x\) is the unknown percentage.
• This proportion compares the ratio \(\frac{x}{100}\) — the unknown percentage — to the ratio \(\frac{17}{68}\) — the known fraction of the number.

To solve for \(x\), we used a technique called cross-multiplication, which is very handy when dealing with proportions.

Cross-Multiplication

Cross-multiplication is a method of solving equations that involve proportions. It's a quick, reliable method for finding an unknown in a fraction.

• To use cross-multiplication, you multiply the numerator of the first fraction by the denominator of the second fraction and vice versa.
• In our exercise, we started with the proportion \(\frac{x}{100} = \frac{17}{68}\).
• Applying cross-multiplication, we got the equation: \(68x = 17 \times 100\).

Cross-multiplication simplifies the problem, turning a proportion into a simple equation (in this case \(68x = 1700\)), which we can easily solve to find \(x\).

Fraction to Percentage Conversion

Converting a fraction to a percentage is a fundamental concept that allows us to express a quantity as a part of 100. This is often done by solving an equation after setting up a proportional relationship.

• In our exercise, we needed to convert the fraction \(\frac{17}{68}\) into a percentage.
• This process was facilitated through solving the proportion: \(\frac{x}{100} = \frac{17}{68}\).
• After cross-multiplying and solving, \(x = \frac{1700}{68}\) was calculated.

We then simplified this to approximately 25, which means \(17\) is approximately 25% of \(68\). This method of conversion is invaluable when you need to interpret fractions in a percentage format.