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Missed the LibreFest? For what total sales will she be able to achieve her goal? Rameen’s heating bill is $5.42 per month plus$1.08 per therm. Check} \text{ the answer in the problem}} &{} \\ {\text{and make sure it makes sense.}} \\{\text{gives the information to find it.}} Read} \text{ the problem.}} &{} \\ {\textbf{Step 2. $$\begin{array} {ll} {\textbf{Step 1. Real world linear equations in action as well as free worksheet that goes hand in hand with this page's real world ,word problems. &{} \\ {\text{If Elliot did 90 jobs, his profit would be}} & {}\\ {\text{60(90)−1,100,or \4,300. Answer} \text{ the the question with a complete sentence.}} &{} \\ {\text{Choose a variable to represent that quantity.}} \\{\textbf{Step 4. His budget for the party is 500. They plan to rent a car from a company that charges 75 a week plus 0.25 a mile. &{n \leq 15}\\ \\{\textbf{Step 6. &{\text{the maximum number of tablets Dawn can buy}} \\ {\textbf{Step 3. Read} \text{ the problem.}} &{\text{the highest rent Emma will qualify for}} \\ {\textbf{Step 3. Pete works at a computer store. Sometimes life gets complicated! What is the highest rent Emma will qualify for? \(\begin{array} {ll} {\textbf{Step 1. It’s easy to think of algebra as an abstract notion that has no use in real life. \end{array}$$. In fact, inequality applications are so common that we often do not even realize we are doing algebra. \\ {\text{to find it.}} &{\text{Elliot must work at least 85 jobs.}} How much should his total sales be for his variable pay option to exceed the fixed amount of $925? Brenda’s best friend is having a destination wedding and the event will last 3 days. Solve} \text{ the inequality.}} Read} \text{ the problem.}} Malik is planning a 6-day summer vacation trip. &{} \\{\textbf{Step 7. &{} \\ {\textbf{Step 2. Josue wants to go on a 10-day road trip next spring. Check} \text{ the answer in the problem}} &{} \\ {\text{and make sure it makes sense.}} For example, how many gallons of gas can be put … Watch the recordings here on Youtube! &{0.25m \leq 125} \\ {} &{m \leq 500 \text{ miles}} \\ \\ \\{\textbf{Step 6. A common goal of most businesses is to make a profit. Matrix mathematics simplifies linear algebra, at least in providing a more compact way to deal with groups of equations in linear algebra. &{60j - 1100 \geq 4000} \\\\ {\textbf{Step 5. \end{array}\). &{\text{The total sales must be more than \$3541.67}} \end{array}\). &{} \\ {\text{Choose a variable to represent it}} &{\text{Let j = the number of jobs.}} If the average weight of one person is 150 pounds, how many people can safely ride the elevator? In fact, inequality applications are so common that we often do not even realize we are doing algebra. Translate.} &{} \\ {} &{\text{The expenses must be less than or equal to}} \\ {} &{\text{the income. &{\text{ less than or equal to \$200.}} 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. &{n \leq 15.74} \\ {\text{But n must be a whole number of tablets,}} &{} \\ {\text{so round to 15.}} \text{ write a sentence that}} &{\text{\$75 plus 0.25 times the number of miles is}} \\{\text{gives the information to find it.}} Real-life examples of linear equations include distance and rate problems, pricing problems, calculating dimensions and mixing different percentages of solutions. Angie has $20 to spend on juice boxes for her son’s preschool picnic. &{\text{Sergio and Lizeth can travel 500 miles}} \\ {} &{\text{and still stay on budget.}} Check} \text{ the answer in the problem}} &{} \\ {\text{and make sure it makes sense.}} Felicity has a calligraphy business. Remember to}} &{500 + 0.12s > 925} \\{\text{convert the percent to a decimal.}} Translate.} &{} \\{\textbf{Step 4. Name} \text{ what we are looking for.}} Tiffany just graduated from college and her new job will pay her$20000 per year plus 2% of all sales. By the end of this section, you will be able to: Before you get started, take this readiness quiz. The context of the application will determine whether we round up or down. Answer} \text{ the answer in the problem}} &{\text{the question with a}} \\ {\text{complete sentence.}} Popular pages @ mathwarehouse.com . The tablets she would like to buy cost $254.12 each, including tax and delivery. &{} \\ {} &{\text{Let s = the total sales.}} In that case, we must round the algebraic solution to a whole number. This is}} &{} \\ {\text{more than \$4,000.}} &{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. &{\text{the number of jobs Elliot needs}} \\ {\textbf{Step 3. Elliot has a landscape maintenance business. Have questions or comments? Dawn won a mini-grant of $4,000 to buy tablet computers for her classroom. The pallet can safely support no more than 900 pounds. Answer} \text{ the the question with a complete sentence.}} Identify} \text{ what we are looking for.}} &{\text{the number of miles Sergio and Lizeth can travel}} \\ {\textbf{Step 3. &{254.12n \leq 4000} \\ {\textbf{Step 5. Name} \text{ what we are looking for.}} \\ {\text{Choose a variable to represent that quantity.}} He has$520 in savings and can earn $30 per driveway shoveling snow. So a}} &{} \\{\text{maximum of 15 tablets at \$254.12}} &{} \\ {\text{seems reasonable.}} Translate.} Real Life Linear Model. What is the maximum number of people Daniel can have at the party? &{} \\{\textbf{Step 7. Identify} \text{ what we are looking for.}} How many driveways must he shovel to have enough money to pay for the trip? How many hours must she babysit to have enough money to pay for the trip? Her monthly expenses are $650. Name} \text{ what we are looking for.}} She expects to pay$350 airfare, $375 for food and entertainment and$60 a night for her share of a hotel room. &{} \\ {\textbf{Step 2. What is the maximum number of tablets Dawn can buy? Sometimes an application requires the solution to be a whole number, but the algebraic solution to the inequality is not a whole number. & {}\\{\textbf{Step 7. Read} \text{ the problem.}} 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.}} \\ {\text{Translate into an inequality. }} &{} \\{\textbf{Step 4. Brenda has $500 in savings and can earn$15 an hour babysitting. &{} \\ {\textbf{Step 7. &{} \\{} &{\text{Emma’s monthly income must be at least}} \\ {\text{First write a sentence that gives the information}} &{\text{three times the rent.}} It will cost him $180 for gas,$450 for food, and $49 per night for a motel. She wants to earn at least$100000 per year. He charges $32 per hour. How many text messages can she use and keep her monthly phone bill no more than$50? How many invitations must she write to earn a profit of at least $2800 per month? Her monthly income will be$5,265. \text{ write a sentence that}} &{\text{\$60 times the number of jobs minus \$1,100 is at least \$4,000.}} &{} \\ {\text{We substitute 27 into the inequality.}} Name} \text{ what we are looking for.}} \text{ write a sentence that}} &{} \\{\text{gives the information to find it.}} Related Links: ... Free Algebra Solver ... type anything in there! &{\$350 + \$375 + \$60(3) \leq \$500 + \$15h} \\\\ {\textbf{Step 5. The trip will cost him $525 for airfare,$780 for food and sightseeing, and $95 per night for the hotel. \\ {\text{Translate into an inequality. &{} \\ {\text{A maximum rent of \$1,755 seems}} &{} \\ {\text{reasonable for an income of \$5,265.}} His monthly expenses are$1,100. Many real-life situations require us to solve inequalities. She charges $2.50 per wedding invitation. Too often students think of algebra as an abstract topic completely disconnected from the real world. It is represented as a rectangular group of rows and columns, such as . Alan is loading a pallet with boxes that each weighs 45 pounds. For what total sales would this new job pay more than his current job which pays$60000? &{} \\\\ {\textbf{Step 5. Solve} \text{ the inequality.}} Legal. Solve Applications with Linear Inequalities. Many real-life situations require us to solve inequalities. &{} \\ {\text{Rounding down the price to \$250,}} &{} \\ {\text{15 tablets would cost \$3750, while}} &{} \\ {\text{If we round the total sales up to}} &{} \\{\text{\$4000, we see that}} &{} \\ {\text{500+0.12(4000) = 980, which is more}} &{} \\ {\text{than \$925.}} &{} \\ {\textbf{Step 2. &{} \\ {} &{\text{Let r = rent}} \\ {\text{Choose a variable to represent that quantity.}}