Question

Translate to an equation and solve. \(14.8 \%\) of 160 is what number?

Short answer

Answer: Approximately 23.68.

Step-by-step solution

Translate to an equation

We can translate this problem into an equation by using the percentage formula: `(Percentage / 100) * Total = Amount` In this case, the percentage is \(14.8\%\) and the total is 160. Let's call the required number "x". So, the equation can be written as: `(14.8 / 100) * 160 = x`

Simplify the equation and solve for x

Now, we can simplify the equation and solve for x: Divide 14.8 by 100: `0.148 * 160 = x` Next, multiply 0.148 by 160: `23.68 = x` So, the required number is 23.68. Therefore, \(14.8\%\) of 160 is approximately 23.68.

Key concepts

Percentage Formula

The percentage formula is a fundamental tool to solve percentage problems. It translates the concept of percentage into mathematical terms. This allows us to solve various problems by framing them as equations. The standard formula to calculate a percentage of a number is:
\[\left( \frac{\text{Percentage}}{100} \right) \times \text{Total} = \text{Amount}\]This formula helps you find what portion a percentage represents of a total amount.

• Percentage: The part that you're calculating, expressed as a number followed by the percent symbol (%).
• Total: The entire amount or number you are considering.
• Amount: The outcome of the calculation or the specific part represented by the percentage.

Equation Translation

Translating words into equations is a critical math skill. It helps in taking a problem in word form and converting it into a math equation that can be solved. In our problem, "14.8% of 160 is what number?", we translate it into a solvable equation:
1. Identify the percentage: **14.8%**2. Identify the total or whole quantity: **160**3. The missing number or the quantity we need to find is represented by **x**.
Using these components, we form the equation: \[\left( \frac{14.8}{100} \right) \times 160 = x\]This step-by-step translation is key in helping solve many mathematical word problems.

Solve for x

Once the equation is set up, the next step is solving for the unknown variable, often represented as **x**. In our equation\[\left( \frac{14.8}{100} \right) \times 160 = x\]Our task is to manipulate the equation to isolate **x** and find its value. In this particular problem, it's accomplished by performing the operations given:

• First, divide 14.8 by 100 to convert the percentage into a decimal: 0.148
• Then, multiply 0.148 by 160
• The result, 23.68, is the value of **x**

Here, **x** represents the number that is 14.8% of 160.

Simplifying Equations

Simplifying equations is an essential process in problem-solving. It involves reducing complexity to show the solution clearly and ensure your calculations are easy to follow. In the equation\[0.148 \times 160 = x\]simplification ensures we find the result without unnecessary steps or errors. Here's how:
1. Calculate simple operations carefully to maintain accuracy: Performing the multiplication precisely gives us the correct result.
2. Check for rounding or approximation where needed, especially with decimals, ensuring clarity in your final answer.
Through simplification, we conclude that **x = 23.68**, our answer to the original problem, showing that 14.8% of 160 is indeed this result.