Question

Linear system of equations and inequalities occur frequently in the solution of problems related to business. Provide an example on the application at the time to get a loan from the bank.

Answer 1

We need an example of Linear Inequalities that would involve the time to the loan from the bank.

A scenario we can create with this is when a person needs to receive the loan in a given amount of time. The problem could go like this:

Rachel needs to take a loan from her bank to pay for her tuition fee. After the final exams, she only has 10 days left to pay for her tuition. After class, she then went to her bank to ask for a loan. Given that the bank would take maximum of 7 days for her to receive the loan, how many days would be left for Rachel to pay her tuition?

With this, we have two inequalities. If we let 'x' be the number of days left for Rachel to pay for her tuition and 'y' is the days that would take the bank to give out the loan:

`\begin{gathered} x+y\leq10 \\ y\leq7 \end{gathered}`

If we substitute the second inequality with the first one, given that the maximum possible value for y is 7, we will get:

`\begin{gathered} x+7\leq10 \\ x\leq10-7 \\ x\leq3 \end{gathered}`

With these, we have the following solutions:

`x\leq3\text{ and }y\leq7`

Therefore, if the bank takes 7 days to give out the loan, Rachel would have a maximum of 3 days to pay her tuition fee.