Question

Solve. After deductions, Wendy's net pay is \(\$ 1016.60 .\) If the total of the deductions was \(32 \%\) of her grosstwo-week salary, what was her gross two- week salary?

Short answer

Answer: Wendy's gross two-week salary is approximately $1495.

Step-by-step solution

Set up an equation

We are given that the total deductions were 32\% of Wendy's gross two-week salary. Let \(x\) be Wendy's gross salary. Then, the deductions can be represented as \(0.32x\). Wendy's net pay is the gross salary minus the deductions, so we can write an equation as follows: \(1016.60 = x - 0.32x\).

Solve for x

To solve for x, we need to combine like terms: \(1016.60 = (1 - 0.32) x\) \(1016.60 = 0.68x\) Now, we will divide both sides of the equation by 0.68: \(x = \frac{1016.60}{0.68}\) \(x \approx 1495\)

Interpret the result

Wendy's gross two-week salary is approximately \$1495.

Key concepts

Percentage Problems

Percentages are a way to express a number as a fraction of 100. It's a valuable skill to convert between percentages, decimals, and fractions.

In problems involving percentages, like the one with Wendy's salary, you're usually given a part of the whole and need to find the overall total. To tackle these problems, you need to understand how percentages are calculated and used to find parts or totals of a given quantity.

• Percentage to Decimal Conversion: To convert a percentage to a decimal, divide by 100. So, 32% becomes 0.32 when converted to a decimal.
• Finding a Part: When you know the percentage and the total, multiply the total by the decimal equivalent of the percentage to find the part.
• Finding the Total: If you know the part and the percentage, divide the part by the decimal equivalent of the percentage to find the total.

Using these conversions, we can say that Wendy's deductions were 32% of her gross salary. In formulaic terms, that translates to: Deductions = 0.32 times Gross Salary.

Net and Gross Salary Calculation

Understanding the difference between net and gross salary is essential when you're dealing with personal finance. Gross salary is the total amount earned before deductions, while net salary is the amount left after deductions.

For example, when calculating Wendy's salary, we start with 32% as the deductions rate. This percentage is applied to the gross salary to determine how much is deducted. Her net salary is what's left after those deductions.

• Gross Salary: Gross salary includes every bit of earnings without subtracting taxes or other deductions.
• Net Salary: Also known as take-home pay, the net salary is gross salary minus all deductions (like taxes, social security, health insurance, etc.).

In equation form, we represented Wendy's scenario as: \[ \text{Net Pay} = \text{Gross Salary} - \text{Deductions} \]To find the gross salary, we solved that equation for the gross amount based on given net pay and the deduction percentage.

Solving Linear Equations

Linear equations are equations of the first degree, meaning they have variables raised only to the power of one. They are fundamental in solving real-life problems such as financial calculations.

In Wendy's problem, we have a linear equation to solve for her gross salary. The equation we set up from the given problem is:\[ 1016.60 = x - 0.32x \]

Here's how we solve it:

• Combine like terms: We consolidate terms to simplify the equation. In this case, combining 'x' and '-0.32x' to simplify it to '0.68x'.
• Isolate the variable: Divide both sides by the coefficient of the variable. For Wendy's equation, divide each side by 0.68 to isolate and calculate 'x', which represents the gross salary.

Essentially, solving linear equations involves balancing the equation, ensuring whatever operation is done to one side is done to the other side, preserving equality. These steps enable you to find unknown variables effectively.