Solving+Problems+Using+Linear+Equations

= Solving Problems Using Linear Equations = = by Nathan Pharr = = Last Updated on 12/14/08 =

=Media File =

This is a video on solving word problems using linear equations =media type="youtube" key="JDmmRVUKQww" height="350" width="429"= =Definitions =

You can not solve every type of practical problem with a simple mathematical procedure or algorithm

=Steps =

1. Read the problem carefully several times and decide what number or numbers are asked for. 2. Chose a variable to represent one of the numbers asked for or described in the problem. A sketch or chart may be helpful. 3. Write an open sentence representing the relationship stated or implied in the problem. 4. Solve the open sentence. 5. Check your result with the requirements stated in the problem.

=**Links** = http://www.purplemath.com/modules/systprob.htm Stapel, Elizabeth. "System-of-Equations Word Problems." __Purplemath__. Available from __. Accessed 14 November 2008

[|example of problems] this is the citation for the page. **http://www.algebra.com/algebra/homework/coordinate/lessons/linear/** **

=Quiz Questions =

the plane in still air.
 * 1) Flying to Kampala with a tailwind a plane averaged 158 km/h. On the return trip the plane only averaged 112 km/h while flying back into the same wind. Find the speed of the wind and the speed of

2) The school that Stefan goes to is selling tickets to a choral performance. On the first day of ticket sales the school sold 3 senior citizen tickets and 1 child ticket for a total of $38. The school took in $52 on the second day by selling 3 senior citizen tickets and 2 child tickets. Find the price of a senior citizen ticket and the price of a child ticket.

3) A boat traveled 210 miles downstream and back. The trip downstream took 10 hours. The trip back took 70 hours. What is the speed of the boat in still water? What is the speed of the current?   4) The state fair is a popular field trip destination. This year the senior class at High School A and the senior class at High School B both planned trips there. The senior class at High School A rented and filled 8 vans and 8 buses with 240 students. High School B rented and filled 4 vans and 1 bus with 54  students. Every van had the same number of students in it as did the buses. Find the number of students in each van and in each bus.  5) The senior classes at High School A and High School B planned separate trips to New York City. The senior class at High School A rented and filled 1 van and 6 buses with 372 students. High School B  rented and filled 4 vans and 12 buses with 780 students. Each van and each bus carried the same number of students. How many students can a van carry? How many students can a bus carry? Answers at the bottom of the page. This is the citation for the quiz questions http://www.kutasoftware.com/FreeWorksheets/Systems%20of%20Equations%20Word%20Problems.pdf****

=Examples = Example #1 The first stage of a rocket burns 28 seconds longer than the second stage. If the total burning time for both stages is 152 seconds, how long does each stage burn?  This is not really about rockets (did the word "rockets" scare you, making the problem more difficult?). It is about numbers. I restate the problem: We have two numbers, one is 28 more than the other, and the sum is 152. No matter how we state the problem in words, algebraically it is x+x+28=152, and we can solve for x (or t, as many people would do). Example #2: In a student election, 584 students voted for one or the other of two candidates for president. If the winner received 122 more votes than the loser, how many votes were cast for each candidate? <span style="color: rgb(254, 53, 22);"> This is the same problem as #1, with different numbers. x+x+122=584. Example #3: How many liters of a 10% solution of acid should be added to 20 liters of a 60% solution of acid to obtain a 50% solution? <span style="color: rgb(254, 53, 22);"> We might state this formula for the use of percent solutions: A=RM, where A is the amount of the substance (acid), R is the ratio (a percentage is a ratio times 100, so we have to divide by 100) of the substance in the mixture, and M is the amount of the mixture (solution). This is just the definition of "ratio" or "percentage." Well, using A=RM, we have a 10% solution and a 60% solution. A1=0.10M1 and A2=0.60(20), and we want to mix them: A1+A2=0.50(M1+20). We can calculate A2, and that gives us two equations with two unknowns (A1 and M1), so we can probably solve for both

this is the citation for the examples. http://www.jimloy.com/algebra/word4.htm

=<span style="color: rgb(37, 15, 235);"> Answers for quiz questions = <span style="font-size: 12pt; color: rgb(255, 10, 10); font-family: Times-Roman;"> 1. Plane: 135 km/h, Wind: 23 km/h <span style="font-size: 12pt; color: rgb(255, 10, 10); font-family: Times-Roman;"> 2. senior citizen ticket: $8, child ticket: $14 <span style="font-size: 12pt; color: rgb(0, 0, 0);"><span style="color: rgb(255, 0, 0);">3. boat: 12 mph, current: 9 mph <span style="font-size: 12pt; color: rgb(255, 10, 10); font-family: Times-Roman;"> 4. Van: 8, Bus: 22 <span style="font-size: 12pt; color: rgb(255, 10, 10); font-family: Times-Roman;"> 5. Van: 18, Bus: 59