Matrix mathematics simplifies linear algebra, at least in providing a more compact way to deal with groups of equations in linear algebra. Real Life Linear Model. &{} \\ {} &{\text{Let n = the number of tablets.}} We also acknowledge previous National Science Foundation support under grant numbers 1246120, 1525057, and 1413739. Check} \text{ the answer in the problem}} &{} \\ {\text{and make sure it makes sense.}} \\ {\text{Translate into an inequality.}} Understanding the history and the practical applications of algebra that are put into use every day might make you see it a little differently. &{} \\ {} &{\text{Let r = rent}} \\ {\text{Choose a variable to represent that quantity.}} &{$254.12\text{ times the number of tablets is no}} \\ {} &{\text{more than \$4000.}} &{\text{The total sales must be more than \$3541.67}} \end{array}\). Translate.} Malik is planning a 6-day summer vacation trip. Solve} \text{ the inequality.}} Daniel wants to surprise his girlfriend with a birthday party at her favorite restaurant. She charges $2.50 per wedding invitation. How many hours must he tutor to have enough money to pay for the trip? &{n \leq 15.74} \\ {\text{But n must be a whole number of tablets,}} &{} \\ {\text{so round to 15.}} Too often students think of algebra as an abstract topic completely disconnected from the real world. &{5265 \geq 3r} \\ {\text{Remember, } a > x\text{ has the same meaning}} &{1755 \geq r} \\ {\text{as }x < a} &{r \leq 1755} \\ {\textbf{Step 6. If the average weight of one person is 150 pounds, how many people can safely ride the elevator? &{} \\{\textbf{Step 4. \end{array}\). Identify} \text{ what we are looking for.}} &{} \\ {\textbf{Step 2. We will read the problem and make sure all the words are understood. &{} \\{\textbf{Step 4. What is the highest rent Emma will qualify for? & {}\\{905 \leq 500 + 15h} &{} \\ {905 \leq 500 + 15(27)} &{} \\ {905 \leq 905} &{} \\ \\{\textbf{Step 7. What is the maximum number of tablets Dawn can buy? Real world linear equations in action as well as free worksheet that goes hand in hand with this page's real world ,word problems. This is}} &{} \\ {\text{more than \$4,000.}} What is the maximum number of packs she can buy? &{} \\ {} &{\text{Let s = the total sales.}} Read} \text{ the problem.}} \(\begin{array} {ll} {\textbf{Step 1. A matrix organizes a group of numbers, or variables, with specific rules of arithmetic. Read} \text{ the problem.}} \text{ write a sentence that}} &{} \\{\text{gives the information to find it.}} &{} \\\\ {\textbf{Step 5. &{\$350 + \$375 + \$60(3) \leq \$500 + \$15h} \\\\ {\textbf{Step 5. & {}\\{\textbf{Step 7. Check} \text{ the answer in the problem}} &{} \\ {\text{and make sure it makes sense.}} Name} \text{ what we are looking for.}} In fact, inequality applications are so common that we often do not even realize we are doing algebra. In fact, inequality applications are so common that we often do not even realize we are doing algebra. In the next example, we will find the number of jobs a small businessman needs to do every month in order to make a certain amount of profit. The cost of airfare plus the}} \\ {} &{\text{cost of food and entertainment and the}} \\ {} &{\text{hotel bill must be less than or equal to the savings}} \\ {} &{\text{plus the amount earned babysitting.}} Her monthly expenses are $650. Angie has $20 to spend on juice boxes for her son’s preschool picnic. \end{array}\). \(\begin{array} {ll} {\textbf{Step 1. &{\text{the number of hours Brenda must babysit}} \\ {\textbf{Step 3. How many boxes can he safely load onto the pallet? Applications of Linear Algebra. Translate.} Have questions or comments? \(\begin{array} {ll} {\textbf{Step 1. One application of linear equations is illustrated in finding the time it takes for two cars moving toward each other at different speeds to reach the same point. \(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\), 3.6: Solve Applications with Linear Inequalities, [ "article:topic", "license:ccby", "showtoc:no", "authorname:openstaxmarecek" ], \( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \) \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\) \(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\), Solve Applications with Linear Inequalities, Solve applications with linear inequalities. Her monthly income will be $5,265. Name} \text{ what we are looking for.}} &{} \\\\ {\textbf{Step 5. &{254.12n \leq 4000} \\ {\textbf{Step 5. &{} \\{\textbf{Step 4. To qualify to rent an apartment, Emma’s monthly income must be at least three times as much as the rent. &{} \\{\textbf{Step 4. &{\text{Elliot must work at least 85 jobs.}} Solve Applications with Linear Inequalities. &{} \\ {\text{A maximum rent of \$1,755 seems}} &{} \\ {\text{reasonable for an income of \$5,265.}} &{\text{The maximum rent is \$1,755.}} &{\text{the highest rent Emma will qualify for}} \\ {\textbf{Step 3. For what total sales would this new job pay more than his current job which pays $60000? Introduction to Matrix Arithmetic. Answer} \text{ the the question with a complete sentence.}} The LibreTexts libraries are Powered by MindTouch® and are supported by the Department of Education Open Textbook Pilot Project, the UC Davis Office of the Provost, the UC Davis Library, the California State University Affordable Learning Solutions Program, and Merlot. If he charges $60 per job, how many jobs must he do to earn a profit of at least $4,000 a month? Answer} \text{ the answer in the problem}} &{\text{the question with a}} \\ {\text{complete sentence.}} Answer} \text{ the the question with a complete sentence.}} Josue wants to go on a 10-day road trip next spring. &{60j - 1100 \geq 4000} \\\\ {\textbf{Step 5. How much money should each family member’s holiday gift cost without going over budget? What is the maximum number of people Daniel can have at the party? The elevator in Yehire’s apartment building has a sign that says the maximum weight is 2,100 pounds. &{\text{Dawn can buy a maximum of 15 tablets.}} Identify} \text{ what we are looking for.}} It’s easy to think of algebra as an abstract notion that has no use in real life. Solve} \text{ the inequality.}} \text{ write a sentence that}} &{\text{\$60 times the number of jobs minus \$1,100 is at least \$4,000.}} Unless otherwise noted, LibreTexts content is licensed by CC BY-NC-SA 3.0. &{} \\ {\text{Choose a variable to represent that quantity.}} &{905 \leq 500 + 15h} \\{} &{405 \leq 15h} \\ {} &{27 \leq h} \\ {} &{h \geq 27} \\ \\{\textbf{Step 6. How many text messages can she use and keep her monthly phone bill no more than $50? Check} \text{ the answer in the problem}} &{} \\ {\text{and make sure it makes sense.}} Emma got a new job and will have to move. Next, we will identify what we are looking for and assign a variable to represent it. &{} \\ {\text{Yes, 75 + 0.25(500) = 200.}} &{} \\ {} &{\text{Let m = the number of miles.}} Each pack of juice boxes costs $2.63. It will cost $42.75 per person for dinner, including tip and tax. Identify} \text{ what we are looking for.}}

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