an employee who is saving for retirement wants the ratio of savings to gross income to be 15%. her employer…

Explanation:

Step1: Define the ratio relationship

The total savings - to - gross income ratio should be 15% or 0.15. The employer contributes $95 and the employee contributes $x$ out of a gross income that we can assume to be the sum of the employee's contribution and some multiple of it (in a general sense of income - related calculations). Let the gross income be considered in terms of the employee's contribution $x$. The employer contributes a fixed $95$ and the employee contributes $x$. The total savings is $95 + x$.

Step2: Set up the equation for the ratio

We know that the ratio of total savings to gross income should be 0.15. If we assume the gross income is related to the employee's contribution $x$, and the total savings is $95 + x$, and we want the ratio $\frac{95 + x}{\text{gross income}}=0.15$. If we assume the gross income is such that the employee's contribution rate plus employer's contribution rate should make up the 15% target rate. The employer contributes a non - percentage based amount of $95$. Let the employee's contribution be $x$. The total savings is $95 + x$. We know that the ratio of the total savings to the amount related to the employee's contribution (which we can think of in terms of $x$) should give us the 15% ratio. The correct equation is $0.15=\frac{95 + x}{x/0.05}$ because if the employee wants to have a 15% total savings rate and the employer contributes $95$, and the employee's contribution rate is 5% of their own contribution $x$ to the gross income, we can set up the equation based on the ratio of total savings to the relevant income amount. Cross - multiplying and simplifying gives the correct relationship.

Answer:

$0.15=\frac{95 + x}{x/0.05}$