Chapter P.7, Problem 39E

Solution

The amount a company can borrow if it wants the ratio of assets to liabilities to be no less than 2.

No more than $\$100000$

Given:

A company has current assets of $200, 000 and current liabilities of $50, 000.

Concept Used:

• If there is the strict inequality symbol $<\text{ or}>$ , then use a parenthesis $\left(\right)$ on the interval
• If there is the inequality symbol $\le \text{ or}\ge$ , then use a bracket $\left[\right]$ on the interval
• To graph the endpoint with strict inequality $<\text{ or}>$, use the open parenthesis or a hollow circle at that endpoint.
• To graph the endpoint with inequality symbol $\le \text{ or}\ge$, use the bracket or a solid circle at that endpoint.
• Multiplying or dividing an inequality by a negative number reverse the inequality sign.

Calculation:

Let the amount borrowed be x .

Since the amount borrowed is added to both current assets and current liabilities, the ratio of assets and liabilities after adding the amount borrowed is $\frac{200000+x}{50000+x}$ .

Since the company wants this ratio to be no less than 2, it follows

  $\begin{array}{c}\frac{200000+x}{50000+x}\ge 2\\ \frac{200000+x}{50000+x}-2\ge 0\\ \frac{200000+x-2\left(50000+x\right)}{50000+x}\ge 0\\ \frac{200000+x-100000-2x}{50000+x}\ge 0\\ \frac{100000-x}{50000+x}\ge 0\\ 100000-x\ge 0\\ -x\ge 100000\\ x\le 100000\end{array}$

Thus, the amount borrow should not be more than $\$100000$ .