Chapter 5.1, Problem 62PFA

(a)

To determine

Match the inequalities can be used to model Marlene`s account activity for Monday.

Answer to Problem 62PFA

Option B is correct.

Explanation of Solution

Given:

On Monday, Marlene with draws $50 from ATM, writes check for her cable bill for $160, and uses her debit card to buy $42.25 worth of groceries. At the end of the day, her account balances is at least $400.

What is the inequalities can be used to model Marlene`s account activity for Monday?

A: x − 202.25 = 350

B: x − 252.25 = 400

C: x = 752.25

D: x − 202.25 > 350

E: x − 252.25 = 400

F: x − 92.25 = 240

Concept Used:

On Monday, Marlene with draws $50 from ATM, writes check for her cable bill for $160, and uses her debit card to buy $42.24 worth of groceries. At the end of the day, her account balances is at least $400.

Total expense of Marlene: $\$\left(50\text{ +}160+42.25\right) =\$252.25$

Let the amount before her expense is $X

Condition given: At the end of the day, her account balances is at least $400.

Inequality: $\text{X }–252.25\ge 400$

Calculation:

Inequality: $\text{X }–252.25\ge 400$

B: x − 252.25 = 400

Option B is correct.

Thus, option B is correct.

(b)

To determine

Find the least amount that Marlene has in her account on Monday before her first transaction.

Answer to Problem 62PFA

At least $\$652.25$

Explanation of Solution

Given:

On Monday, Marlene with draws $50 from ATM, writes check for her cable bill for $160, and uses her debit card to buy $42.24 worth of groceries. At the end of the day, her account balances is at least $400.

Concept Used:

Find the least amount that Marlene has in her account on Monday before her first transaction.

To find the least amount in her account on Monaday before any transection just only add the amount she has already spend with the rest amount after spending.

Inequality: $\text{X }–252.25\ge 400$

Calculation:

  $\begin{array}{l}\text{X }–252.25\ge 400\\ \text{X }–252.25+252.25\ge 400+252.25\\ \text{X}\ge 652.25\end{array}$$652.25 The least amount that Marlene has in her account on Monday before her first transaction is at least $\$652.25$

Thus, the amount in her account on Monday before her first transaction is at least $\$652.25$

(c)

To determine

Write an inequality that models Marlene`s balance before her first transaction

Answer to Problem 62PFA

  $\text{X}\ge 652.25$

Explanation of Solution

Given:

On Monday, Marlene with draws $50 from ATM, writes check for her cable bill for $160, and uses her debit card to buy $42.24 worth of groceries. At the end of the day, her account balances is at least $400.

Concept Used:

Let the amount before her expense is $X

Inequality: $\text{X}\ge 652.25$

Calculation:

Inequality: $\text{X}\ge 652.25$

Thus, the inequality that models Marlene`s balance before her first transaction is $\text{X}\ge 652.25$

(d)

To determine

Write the solution set in set builder notation.

Answer to Problem 62PFA

  $\{\text{X}|\text{X}\ge 652.25\}$

Explanation of Solution

Given:

On Monday, Marlene with draws $50 from ATM, writes check for her cable bill for $160, and uses her debit card to buy $42.24 worth of groceries. At the end of the day, her account balances is at least $400.

Use set builder notation to write your answer to part C.

Concept Used:

Use set builder notation to write your answer to part C.

Set Builder Notation: $\{\text{X}|\text{X}\ge 652.25\}$

Thus, the set Builder Notation: $\{\text{X}|\text{X}\ge 652.25\}$

(e)

To determine

Graph the solution on number line.

Answer to Problem 62PFA

Explanation of Solution

Given:

On Monday, Marlene with draws $50 from ATM, writes check for her cable bill for $160, and uses her debit card to buy $42.24 worth of groceries. At the end of the day, her account balances is at least $400.

Concept Used:

Here is a summary of how to graph inequalities:

1) Draw a number line.2) Put either an open circle or a closed dot above the number given.

For = and = , use a closed dot to indicate the number itself is part of the solution.

For < and >, use an open circle to indicate the number itself is not part of the solution.

3) Choose which way the arrow should go. Either think about which numbers would be part of the solution. Or, as long as the variable is listed first, you can just look at the symbol

For = and <, the arrow points down to the left.

For = and >, the arrow points up to the right.

A closed, or shaded, circle is used to represent the inequalities greater than or equal to ( $\ge$ ) or less than or equal to ( $\le$ ). The point is part of the solution.

Graph the inequality $\text{X}\ge 652.25$ on a number line.

  

Thus, inequality $\text{X}\ge 652.25$ and the graph is on the number line.