Chapter 3.2, Problem 75PPE

To determine

To find: The amount can be deposited in account by the end of the month to avoid paying the service fee.

Answer to Problem 75PPE

The amount can be deposited in account by the end of the month to avoid paying the service fee $\$88.74$

Explanation of Solution

Given information:

The checking account balance at the end of each month = $\text{\$}500$ .

Current balance = $\$\mathrm{536.45.}$

The debit card expenditure = $\$\mathrm{125.19.}$

Calculation:

To avoid a service fee, checking account balance must be at least $\text{\$}500$ Current balance is $\$\mathrm{536.45.}$ Also, $\$\mathrm{125.19.}$ is spending using debit card.

Let $\$x$ represent the amount to be deposited to avoid service fee. Then the problem can be modeled as:

Current balance minus debited amount plus amount deposited is at least $\text{\$}500$ .

Therefore,

  $\begin{array}{r}\hfill 536.45-125.19+x\ge 500\\ \hfill 411.26+x\ge 500\end{array}$

  $4+1.26-41+.26+x\ge 500-411.26(\text{subtract 411}\text{.26 from each side})$

  $\ge 88.74$ (simplify)

Hence avoid a service fee,, at least $\$88.74$ is to be deposited

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