3.4. System of Equation Word Problems College Algebra 3.4. System of Equation Word Problems

Do Now: Solve the system using SUBSTITUTION: 2𝑥−𝑦=3 −8𝑥+4𝑦=−12 Solve the system using ELIMINATION: −14𝑥+5𝑦=−13 6𝑥−3𝑦=9

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So….. We know how to solve systems of equations by graphing, substitution and elimination– let’s bring this to the real world! Let’s look at work problems!

Example One: The sum of two numbers is 25 and the difference between them is 3. Find the two numbers.

Example Two: The sum of two numbers is 6. Twice the first number plus half the second is 0. Find the two numbers.

You Try! The sum of two numbers is 21. Their difference is 5. What are the numbers? The sum of two numbers is 5. Three times the first number plus five is equal to negative one times half of the second number. What are the two numbers?

Example Three: Lea and Cody are selling wrapping paper for a school fundraiser. Customers can buy plain wrapping paper or shiny wrapping paper. Lea sells 2 rolls of plain wrapping paper and 6 rolls of shiny wrapping paper for a total of $144.00. Cody sells 10 rolls of plain wrapping paper and 6 rolls of shiny wrapping paper for a total of $240.00. Find the cost of one roll of plain wrapping paper.

Example Four: The senior classes at high school A and high school B planned separate trips to the local amusement park. The senior class at High School A rented and filled 4 vans and 5 buses with 304 students. High school B rented and filled 4 vans and 7 buses with 408 students. Assume that every van and bus can hold the same number of students. Find the number of students that can held in both a van and a bus.

Example Five Heather and Nina are selling cookie dough for a school fundraiser. Customers can buy packages of white chocolate chip cookie dough and gingerbread cookie dough. Heather sells 5 packages of white chocolate chip cookie dough and 3 packages of gingerbread cookie dough for a total of $76. Nina sells 14 packages of white chocolate chip cookie dough and 3 packages of gingerbread cookie dough for a total of $121. If Ms. Stonebraker buys two packages of white chocolate chip cookie dough and one package of gingerbread, how much will it cost her?

You Try! The school that Billy goes to is selling tickets to a play. On the first day of ticket sales the school sold 11 senior citizen tickets and 9 student tickets for a total of $208.00. The second day of sales brought in $190.00 by selling 11 senior citizen tickets and 6 student tickets. If you, your grandma and your young brother go to the show, how much will you spend on tickets?

Do Now: You buy seven bags of gummy bears and three bags of chocolate for $22.00. Your friend spends $8.00 on three bags of gummy bears and one bag of chocolate. If Ms. Stonebraker wants to buy two bags of gummy bears and three bags of chocolate, how much money will she spend? The sum of two numbers is 25. The first number is four more than twice the second number. What are the two numbers?

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Example Six- Slightly Different: At a grocery store, apples cost $2.00 a pound and oranges cost $3.00 a pound. If Ms. Stonebraker bought 8 pounds of fruit and spent $18.00, how many pounds of apples did she end of buying?

Example Seven: A test has 20 questions and is worth a total of 100 points. The test consists of True/False questions worth 3 points each and short answer questions worth 11 points each. How many short answer questions were there on the test?

Example Eight: Over the weekend my niece and I went to the park and we saw ducks and squirrels. My niece counted 12 heads total and I counted 30 legs. How many ducks were there at the park?

Example Nine: The Celtics scored a total of 80 points in a basketball game against the Bulls. They made a total of 37 shots. Some of the shots were 2-point shots and others were 3-point shots. How many three point shots did the Celtics make during the game?

Word Problems Generalized: Each time– start by making a table with the given information so you can organize your thoughts THEN– create two equations Last- SOLVE! Finish by INTERPRETING your solution within the context of the problem/units!

You Try! 1. Timmy and Tori took a road trip together. Timmy consistently drove 60 mph and Tori drove 40 mph. They switched off driving periodically throughout the trip. If together they drove a total distance of 270 miles in 5 hours, how long did Timmy drive? 2. A total of 78 seats for a concert are sold, producing a total revenue of $483.00. If seats cost either $2.50 or $10.50, how many $2.50 seats were sold?

Do Now: Braintree High School spent a total of $4, 650 last year to purchase 100 new calculators. Some calculators were TI-83 which cost $105.00 each, and some were basic calculators that cost $15.00 each. How many of each kind of calculator was purchased? Billy went to Coffee Express and ordered three coffees and two muffins and paid $7.00. Later, Sammy went to Coffee Express and spent $8.00 buying four muffins and two coffees. If Ms. Stonebraker goes to Coffee Express and orders one muffin and two coffees, how much will it cost her?

Example Ten: Careful with Coins! Sara has a jar filled with 135 coins, which consists only of quarters and nickels. If Sara has a total of $22.75 in the jar, determine the number of nickels that Sara has in the jar.

You Try! Ms. Stonebraker has quarters and dimes in her desk. She has a total of 23 coins, which total $5.00. How many quarters does she have in her desk?

Example Eleven: Slightly Different: Shirley is going to have the exterior of her home painted. Tim’s painting charges $250 plus $14.00 per hour. Colorful Paints charges $22 per hour. How many hours would the job need to be for both companies’ cost to be equal?

Example Twelve: Tracey has been offered two different summer jobs. The first, as a nanny, pays $15.00 an hour with a bonus of $100.00 at the end of the summer. The other potential job, as a maid, pays $20.00 an hour. How many hours must Tracey work this summer to make equal amounts of money at each job?

Example Thirteen: Shelly worked 12 more hours than Julie. They worked a total of 72 hours. How many hours did both girls work?

You Try! Tracey is looking at two different travel agencies to plan her vacation. ABC Travel offers a plane ticket for $295 and a rental car for $38 per day. M & N Travel offers a plane ticket for $350 and a rental car for $33 per day. After how many days will both rental costs be equal? The population of a city is 2,500. If the number of males is 240 more than the number of females, how many males and females are there in the city? English is spoken as the first or primary language in 78 more countries than Farsi is spoken as the first language. Together, English and Farsi are spoken as a first language in 130 countries. In how many countries is English spoken as the first language? In how many countries is Farsi spoken as the first language?

Practice Problems Try some on your own/in your table groups As always don’t hesitate to ask questions if you are confused OR talk to your tablemates! They are your greatest resource!