Solving Linear System of Equa5ons Word Problems
Remember:
Example  #1  Chapter 4_Solving Linear Systems Word Problems Now that we have techniques for solving systems we can set up our word problems with two variables. If we use two variables we will need two equations. With this in mind, look for two relationships when reading the questions. A. Number Problems Last season two running backs on the Steelers football team rushed for a combined total of 1550 yards. One rushed 4 times as many yards as the other. How many yards were rushed by each one?
The set-up determines the method we will choose to solve the system. Since the y variable was isolated the easiest method to choose was the substitution method. Although, it does not matter which method we choose the answer will be the same. A particular Algebra text has a total of 1382 pages which is broken up into two parts. The second part of the book has 64 more pages than the first part. How many pages are in each part of the book?
Example  #1  Chapter 4_Solving Linear Systems Word Problems Now that we have techniques for solving systems we can set up our word problems with two variables. If we use two variables we will need two equations. With this in mind, look for two relationships when reading the questions. A. Number Problems Last season two running backs on the Steelers football team rushed for a combined total of 1550 yards. One rushed 4 times as many yards as the other. How many yards were rushed by each one?
The set-up determines the method we will choose to solve the system. Since the y variable was isolated the easiest method to choose was the substitution method. Although, it does not matter which method we choose the answer will be the same. A particular Algebra text has a total of 1382 pages which is broken up into two parts. The second part of the book has 64 more pages than the first part. How many pages are in each part of the book?
Example  #1  Chapter 4_Solving Linear Systems Word Problems Now that we have techniques for solving systems we can set up our word problems with two variables. If we use two variables we will need two equations. With this in mind, look for two relationships when reading the questions. A. Number Problems Last season two running backs on the Steelers football team rushed for a combined total of 1550 yards. One rushed 4 times as many yards as the other. How many yards were rushed by each one?
The set-up determines the method we will choose to solve the system. Since the y variable was isolated the easiest method to choose was the substitution method. Although, it does not matter which method we choose the answer will be the same. A particular Algebra text has a total of 1382 pages which is broken up into two parts. The second part of the book has 64 more pages than the first part. How many pages are in each part of the book?
Example  #1  Chapter 4_Solving Linear Systems Word Problems Now that we have techniques for solving systems we can set up our word problems with two variables. If we use two variables we will need two equations. With this in mind, look for two relationships when reading the questions. A. Number Problems Last season two running backs on the Steelers football team rushed for a combined total of 1550 yards. One rushed 4 times as many yards as the other. How many yards were rushed by each one?
The set-up determines the method we will choose to solve the system. Since the y variable was isolated the easiest method to choose was the substitution method. Although, it does not matter which method we choose the answer will be the same. A particular Algebra text has a total of 1382 pages which is broken up into two parts. The second part of the book has 64 more pages than the first part. How many pages are in each part of the book?
Example  #2  Chapter 4_Solving Linear Systems
Word Problems
The idea behind distance problems, sometimes called uniform motion problems, is to organize the given data. First identify the variables then try to fill in the chart with the appropriate values. Sometimes your set up can come from columns in the chart and other times the set up will come from the rows. Remember D r t . F. Uniform Motion Problems An executive traveled 1930 miles by car and plane. He drove to the airport at an average speed of 60 mph and the plane averaged 350 mph. The total trip took 8 hours. How long did it take to get to the airport?
A boat traveled 24 miles downstream in 2 hours. The return trip took twice as long. What is the speed of the boat in still water?
Word problems take practice. Be sure to do all of the assigned word problems and review them often. Do not plan on skipping them on the exams. That is not a winning strategy. Usually, once we set our word problems up correctly, the algebra is easier than
Example  #2  Chapter 4_Solving Linear Systems
Word Problems
The idea behind distance problems, sometimes called uniform motion problems, is to organize the given data. First identify the variables then try to fill in the chart with the appropriate values. Sometimes your set up can come from columns in the chart and other times the set up will come from the rows. Remember D r t . F. Uniform Motion Problems An executive traveled 1930 miles by car and plane. He drove to the airport at an average speed of 60 mph and the plane averaged 350 mph. The total trip took 8 hours. How long did it take to get to the airport?
A boat traveled 24 miles downstream in 2 hours. The return trip took twice as long. What is the speed of the boat in still water?
Word problems take practice. Be sure to do all of the assigned word problems and review them often. Do not plan on skipping them on the exams. That is not a winning strategy. Usually, once we set our word problems up correctly, the algebra is easier than
Example  #2  Chapter 4_Solving Linear Systems
Word Problems
The idea behind distance problems, sometimes called uniform motion problems, is to organize the given data. First identify the variables then try to fill in the chart with the appropriate values. Sometimes your set up can come from columns in the chart and other times the set up will come from the rows. Remember D r t . F. Uniform Motion Problems An executive traveled 1930 miles by car and plane. He drove to the airport at an average speed of 60 mph and the plane averaged 350 mph. The total trip took 8 hours. How long did it take to get to the airport?
A boat traveled 24 miles downstream in 2 hours. The return trip took twice as long. What is the speed of the boat in still water?
Word problems take practice. Be sure to do all of the assigned word problems and review them often. Do not plan on skipping them on the exams. That is not a winning strategy. Usually, once we set our word problems up correctly, the algebra is easier than
Example  #2  Chapter 4_Solving Linear Systems
Word Problems
The idea behind distance problems, sometimes called uniform motion problems, is to organize the given data. First identify the variables then try to fill in the chart with the appropriate values. Sometimes your set up can come from columns in the chart and other times the set up will come from the rows. Remember D r t . F. Uniform Motion Problems An executive traveled 1930 miles by car and plane. He drove to the airport at an average speed of 60 mph and the plane averaged 350 mph. The total trip took 8 hours. How long did it take to get to the airport?
A boat traveled 24 miles downstream in 2 hours. The return trip took twice as long. What is the speed of the boat in still water?
Word problems take practice. Be sure to do all of the assigned word problems and review them often. Do not plan on skipping them on the exams. That is not a winning strategy. Usually, once we set our word problems up correctly, the algebra is easier than
Prac5ce  #1  The set-up determines the method we will choose to solve the system. Since the y variable was isolated the easiest method to choose was the substitution method. Although, it does not matter which method we choose the answer will be the same. A particular Algebra text has a total of 1382 pages which is broken up into two parts. The second part of the book has 64 more pages than the first part. How many pages are in each part of the book?
Problems Solved!
4.4 - 1
Prac5ce #2
Chapter 4_Solving Linear Systems
Word Problems
B. Mixture Problems Dennis mowed his next door neighbor’s lawn for a handful of dimes and nickels, 80 coins in all. Upon completing the job he counted out the coins and it came to $6.60. How many of each coin did he earn?
On Monday Joe bought 10 cups of coffee and 5 doughnuts for his office at the cost of $16.50. It turns out that the doughnuts were more popular than the coffee. On Tuesday he bought 5 cups of coffee and 10 doughnuts for a total of $14.25. How much was each cup of coffee?
A bartender wishes to mix an 8 ounce drink with a 20% alcohol content. He has two liquors, one with a 50% alcohol content and another with 10%. How much of each liquor does he need to mix together?
Prac5ce  #3  On Monday Joe bought 10 cups of coffee and 5 doughnuts for his office at the cost of $16.50. It turns out that the doughnuts were more popular than the coffee. On Tuesday he bought 5 cups of coffee and 10 doughnuts for a total of $14.25. How much was each cup of coffee?
A bartender wishes to mix an 8 ounce drink with a 20% alcohol content. He has two liquors, one with a 50% alcohol content and another with 10%. How much of each liquor does he need to mix together?
A common er put = .20 her alcohol conte be 20% of 8
Problems Solved!
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Prac5ce  #4  A bartender wishes to mix an 8 ounce drink with a 20% alcohol content. He has two liquors, one with a 50% alcohol content and another with 10%. How much of each liquor does he need to mix together?
A common er put = .20 her alcohol conte be 20% of 8 o
Problems Solved!
4.4 - 2
Prac5ce  #5  Chapter 4_Solving Linear Systems
Word Problems
C. Geometry Problems Two angles are supplementary. The larger angle is 48 degrees more than 10 times the smaller angle. Find the measure of each angle.
Supplementary an add to 180 degree
Two angles are complementary. The larger angle is 3 degrees less than twice the measure of the smaller angle. Find the measure of each angle.
Complementary a add to 90 degrees
The perimeter of a rectangular garden is 62 feet. The length is 1 foot more than twice the width. Find the dimension of the garden.
Prac5ce  #6  Two angles are complementary. The larger angle is 3 degrees less than twice the measure of the smaller angle. Find the measure of each angle.
Complementary a add to 90 degrees
The perimeter of a rectangular garden is 62 feet. The length is 1 foot more than twice the width. Find the dimension of the garden.
Problems Solved!
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Prac5ce  #7  The perimeter of a rectangular garden is 62 feet. The length is 1 foot more than twice the width. Find the dimension of the garden.
Problems Solved!
4.4 - 3
Prac5ce #8
Chapter 4_Solving Linear Systems
Word Problems
E. Interest Problems Sally’s $1800 savings is in two accounts. Her total interest for the year was $93 from one account earning 6% annual interest and another earning 3%. How much does she have in each account?
When setting up these word problems look for totals. The above example is very typical, notice that one on the equations consists of the total amount invested, x + y = 1800. The other equation represents the total amount of interest for the year, .03x +.06y = 93. Two linear equations allow you to solve for the variables. Also notice that it is wise to identify your variables every time. This focuses your efforts and aids us in finding the solution. It also tells us what our answers mean at the end. Millicent has $10,000 invested in two accounts. For the year she earned $535 more in interest from her 7% Mutual Fund account than she did from her 4% CD. How much does she have in each account?
notice that one on the equations consists of the total amount invested, x + y = 1800. The other equation represents the total amount of interest for the year, .03x +.06y = 93. Two linear equations allow you to solve for the variables.
Prac5ce  #9 Â
Also notice that it is wise to identify your variables every time. This focuses your efforts and aids us in finding the solution. It also tells us what our answers mean at the end. Millicent has $10,000 invested in two accounts. For the year she earned $535 more in interest from her 7% Mutual Fund account than she did from her 4% CD. How much does she have in each account?
Always check to make sure your answer makes sense in terms of the word problem. If you come up with an answer of, say x = 20,000 in the problem above you know this is unreasonable since the total amount is 10,000. At that point you should first go back and check your set-up then check your algebra steps from there.
Problems Solved!
4.4 - 4
Prac5ce  #10  A boat traveled 24 miles downstream in 2 hours. The return trip took twice as long. What is the speed of the boat in still water?
Word problems take practice. Be sure to do all of the assigned word problems and review them often. Do not plan on skipping them on the exams. That is not a winning strategy. Usually, once we set our word problems up correctly, the algebra is easier than the other problems.
Problems Solved!
4.4 - 5
Notes: Regression – GeMng an equa5on from a Table 1. 2. 3. 4. 5. 6. 7. 8. 9.
Open a New Document 4. Add Lists and Spreadsheet In cell A enter “x” In cell B enter “y” Copy the data from the table into the Spreadsheet Press Menu Press 3. Data Press 9. Quick Graph Change X-‐axis and Y-‐axis labels so that they are correct, place cursor in box near label and click to see op5ons, choose correct op5on 10. Iden5fy the parent func5on of the graph 11. While in Quick Graph, Press Menu 12. Press 4. Analyze 13. Press 6. Regression 14. Choose the correct Parent Func5on to model • 1: Show Linear (mx+b) • 4: Show Quadra5c • 8: Show Exponen5al • 9: Show Logarithmic 15. Equa5on for func5on is now displayed on the screen.
Parent Func5ons:
Problem #1 Given the tables for two func5on below, find the following: • The solu5on(s) to the system of equa5ons • The Domain and Range of each func5on. • Iden5fy the transla5on of func5on from the parent func5on. ex: x transla5on: -‐3; y transla5on: +2; reflected of the y axis
x
y
x
y
-‐5
-‐3
-‐5
-‐16
-‐2
0
-‐2
-‐7
1
3
1
2
4
6
4
11
Problem #2 Given the tables for two func5on below, find the following: • The solu5on(s) to the system of equa5ons • The Domain and Range of each func5on. • Iden5fy the transla5on of func5on from the parent func5on. ex: x transla5on: -‐3; y transla5on: +2; reflected of the y axis
x
y
x
y
-‐7
-‐18.5
-‐5
76
-‐4
-‐9.5
-‐2
16
3
11.5
1
-‐8
6
20.5
4
4
Problem #3 Given the tables for two func5on below, find the following: • The solu5on(s) to the system of equa5ons • The Domain and Range of each func5on. • Iden5fy the transla5on of func5on from the parent func5on. ex: x transla5on: -‐3; y transla5on: +2; reflected of the y axis
x
y
x
y
-‐4
-‐4
-‐3
-‐2.96296
-‐2
-‐3
-‐2
-‐2.88889
4
0
3
24
6
1
7
2184
Problem #4 Given the tables for two func5on below, find the following: • The solu5on(s) to the system of equa5ons • The Domain and Range of each func5on. • Iden5fy the transla5on of func5on from the parent func5on. ex: x transla5on: -‐3; y transla5on: +2; reflected of the y axis
x
y
x
y
-‐4
6
-‐3
1
-‐2
-‐2
-‐2
7
4
22
3
-‐23
6
46
7
-‐119
Problem #5 Given the tables for two func5on below, find the following: • The solu5on(s) to the system of equa5ons • The Domain and Range of each func5on. • Iden5fy the transla5on of func5on from the parent func5on. ex: x transla5on: -‐3; y transla5on: +2; reflected of the y axis
x
y
x
y
-‐4
0
-‐5
.25
-‐2
-‐5
-‐1
4
4
28
2
32
6
55
7
1024
Problem #6 Given the tables for two func5on below, find the following: • The solu5on(s) to the system of equa5ons • The Domain and Range of each func5on. • Iden5fy the transla5on of func5on from the parent func5on. ex: x transla5on: -‐3; y transla5on: +2; reflected of the y axis
x
y
x
y
-‐4
14
-‐5
-‐16
-‐2
6
-‐1
-‐0.8
4
-‐18
2
10.6
6
-‐26
7
29.6
Problem #7 Given the tables for two func5on below, find the following: • The solu5on(s) to the system of equa5ons • The Domain and Range of each func5on. • Iden5fy the transla5on of func5on from the parent func5on. ex: x transla5on: -‐3; y transla5on: +2; reflected of the y axis
x
y
x
y
-‐4
-‐9
-‐5
#UNDEF
-‐2
-‐9
-‐1
1.58496
4
39
2
2.58496
6
71
7
3.45943
Problem #8 Given the tables for two func5on below, find the following: • The solu5on(s) to the system of equa5ons • The Domain and Range of each func5on. • Iden5fy the transla5on of func5on from the parent func5on. ex: x transla5on: -‐3; y transla5on: +2; reflected of the y axis
x
y
x
y
-‐4
4
-‐5
#UNDEF
-‐2
3
-‐1
#UNDEF
4
0
2
0.30103
6
-‐1
7
0.845098