Question
A clothing store has current liabilities of
raise funds to expand their business, they want to take out a short-term loan. What is the
maximum amount they can borrow if their current ratio is to be no less than 2.6 ?
raise funds to expand their business, they want to take out a short-term loan. What is the
maximum amount they can borrow if their current ratio is to be no less than 2.6 ?
Ask by Pollard Romero. in South Africa
Mar 28,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The clothing store can borrow a maximum of
Solution
To determine the maximum amount the clothing store can borrow, we need to calculate the current ratio and then find the maximum amount they can borrow while maintaining a current ratio of at least 2.6.
Given:
- Current liabilities =
- Current assets =
The current ratio is calculated as:
Let’s calculate the current ratio:
Now, we need to find the maximum amount they can borrow while maintaining a current ratio of at least 2.6. Let’s denote the maximum amount they can borrow as
The new current ratio after borrowing
We want this new current ratio to be at least 2.6, so we set up the inequality:
Now, we can solve this inequality to find the maximum amount they can borrow.
Solve the inequality by following steps:
Solve the inequality by following steps:
- step0: Solve the inequality by testing the values in the interval:
- step1: Find the domain:
- step2: Move the expression to the left side:
- step3: Subtract the terms:
- step4: Set the numerator and denominator of
equal to 0
- step5: Calculate:
- step6: Determine the test intervals:
- step7: Choose a value:
- step8: Test the chosen value:
- step9: Include the critical value:
- step10: The final solution is
- step11: Check if the solution is in the defined range:
- step12: Find the intersection:
The maximum amount the clothing store can borrow while maintaining a current ratio of at least 2.6 is.
Therefore, the maximum amount they can borrow is
Answered by UpStudy AI and reviewed by a Professional Tutor
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Simplify this solution Beyond the Answer
To determine the maximum amount the clothing store can borrow while maintaining a current ratio of at least 2.6, we start with the formula for the current ratio, which is:
Currently, the store has current liabilities of
Setting up the inequality for the current ratio:
Cross-multiplying gives:
Expanding and simplifying the right-hand side:
Rearranging to isolate
Calculating the maximum
Therefore, the maximum amount they can borrow while maintaining a current ratio of at least 2.6 is
