Q. 317 Reiko needs to mail her Christma... [FREE SOLUTION]

91影视

Elementary Algebra

Lynn Marecek, MaryAnne Anthony-Smith

$Math Studyset 91影视 Explanations$ Math

2nd Edition 路 1240 pages

ISBN: 9780998625713

Chapter 5: Q. 317 (page 673)

Reiko needs to mail her Christmas cards and packages and wants to keep her mailing costs to no more than $$500$ . The number of cards is at least $4$ more than twice the number of packages. The cost of mailing a card (with pictures enclosed) is $$ 3$ and for a package the cost is $$ 7$ .
鈸� Write a system of inequalities to model this situation.
鈸� Graph the system.
鈸� Can she mail $60$ cards and $26$ packages?
鈸� Can she mail $90$ cards and $40$ packages?

Short Answer

Expert verified

Part 鈸� System of inequalities to model this situation is: $\{\begin{cases} c 鈮� 2 p + 4 \\ 3 c + 7 p 鈮� 500 \end{cases}$

Part 鈸� Graph of the system of inequalities:

鈸� Reiko can mail $60$ cards and $26$ packages.

鈸� Reiko cannot mail $90$ cards and $40$ packages.

Step by step solution

Part (a) Step 1. Finding the system of inequalities

Let, $c$ be the number of cards and $p$ be the number of packages Reiko wants to mail.

The number of cards is at least $4$ more than twice the number of packages. So, the inequality is: role="math" localid="1653353139387" $c 鈮� 2 p + 4$

The cost of mailing a card is $$ 3$ , cost for mailing a package is $$ 7$ and Reiko does not want to spend more than $$ 500$ . So, the inequality is: $3 c + 7 p 鈮� 500$ .

The system of inequalities is: $\{\begin{cases} c 鈮� 2 p + 4 \\ 3 c + 7 p 鈮� 500 \end{cases}$

Part (b) Step 1. Graphing the system of inequalities

Below is the graph of the system of inequalities: $\{\begin{cases} c 鈮� 2 p + 4 \\ 3 c + 7 p 鈮� 500 \end{cases}$

Part (c) Step 1. Finding whether Reiko can mail 60 cards and 26 packages

As the point $(26, 60)$ is in the double shaded region of the graph, so, Reiko can mail $60$ cards and $26$ packages.

Part (d) Step 1. Finding whether Reiko can mail 90 cards and 40 packages

As the point $(40, 90)$ is not in the double shaded region of the graph, so, Reiko cannot mail $90$ cards and $40$ packages.

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91影视

Short Answer

Step by step solution

Part (a) Step 1. Finding the system of inequalities

Part (b) Step 1. Graphing the system of inequalities

Part (c) Step 1. Finding whether Reiko can mail 60 cards and 26 packages

Part (d) Step 1. Finding whether Reiko can mail 90 cards and 40 packages

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