Chapter 0.12, Problem 4E

(a)

To determine

Write and solve an inequality that shows how much money she can spend that month after buying a concert ticket.

Answer to Problem 4E

Lupe can spend that month after buying a concert ticket no more than $15.

Explanation of Solution

Given:

Lupe`s allowance for the month is $60. She wants to go to a concert for which a ticket costs $45.

Concept Used:

Let m represents how much money she can spend that month after buying a concert ticket.

The inequality: $m+45\le 60$

Calculation:

The inequality: $m+45\le 60$

Solve for m:

  $\begin{array}{l}m+45\le 60\\ m+45-45\le 60-45\\ m\le 15\end{array}$

Lupe can spend that month after buying a concert ticket no more than $15.

Thus, Lupe can spend that month after buying a concert ticket no more than $15.

(b)

To determine

Write and solve an inequality that shows how much she can spend both these purchases and the concert ticket.

Answer to Problem 4E

Lupe can spend no more than $3.01for both these purchases and the concert ticket.

Explanation of Solution

Given:

Lupe`s allowance for the month is $60. She wants to go to a concert for which a ticket costs $45.

She spends $9.99 on music downloads and $2 on lunch in the cafeteria. Write and solve an inequality that shows how much she can spend either these purchases or the concert ticket.

Concept Used:

Let m represents how much money she can spend both these purchases and the concert ticket.

The inequality: $m+45+9.99+2\le 60$

Calculation:

The inequality: $m+45+9.99+2\le 60$

Solve for m:

  $\begin{array}{l}m+45+9.99+2\le 60\\ m+56.99\le 60\\ m+56.99-56.99\le 60-56.99\\ m\le 3.01\end{array}$

Thus, Lupe can spend no more than $3.01for both these purchases and the concert ticket.

(c)

To determine

Find what mathematical practice you have used to solve this problem.

Explanation of Solution

Given:

Lupe`s allowance for the month is $60. She wants to go to a concert for which a ticket costs $45.

She spends $9.99 on music downloads and $2 on lunch in the cafeteria. Write and solve an inequality that shows how much she can spend either these purchases or the concert ticket.

Concept Used:

Step 1: make the inequality equation.

Step 2 : Subtract the numbers to both sides.

Step 3: Simplify.

Follow all the rules for solving the inequality.