1. System of Equations WORD PROBLEMS Name Apr 11, 2011 1. Problem Solving Steps 1.What are you trying to find? 2.What do you know? Given in the problem? From formulas and prior knowledge? 3. How will you solve the problem? 4. Did you answer the original question? ALWAYS use these steps when solving word problems:

2. System of Equations WORD PROBLEMS Name Apr 11, 2011 2. Example 1 1.What are you trying to find? The number of adults and children 2.What do you know? Given in the problem? Adults and Children; 20 people total Adult ticket price = $10 Child ticket price = $5 Total bill is $120 A bunch of families are going to the movies. There are 20 people total. An adult ticket costs $10 and a child ticket costs $5. The total bill is $120. How many adults and how many children go to the movie?

3. System of Equations WORD PROBLEMS Name Apr 11, 2011 2. Example 1 From formulas and prior knowledge? Let A = Adults and C = Children We can setup a system of equations 3. How will you solve the problem? Equation 1: Total People: A + C = 20 Equation 2: Total Cost: 10A + 5C = 120 We need to adjust the first equation: -5(A + C = 20) -5A – 5C = -100 A bunch of families are going to the movies. There are 20 people total. An adult ticket costs $10 and a child ticket costs $5. The total bill is $120. How many adults and how many children go to the movie?

4. System of Equations WORD PROBLEMS Name Apr 11, 2011 2. Example 1 3. How will you solve the problem? Equation 1: Total People: A + C = 20 Equation 2: Total Cost: 10A + 5C = 120 -5A – 5C = -100 10A + 5C = 120 5A = 20 4 AdultsA = 4 16 Children 4 + C = 20 C = 16 A bunch of families are going to the movies. There are 20 people total. An adult ticket costs $10 and a child ticket costs $5. The total bill is $120. How many adults and how many children go to the movie?

5. System of Equations WORD PROBLEMS Name Apr 11, 2011 2. Example 1 4. Did you answer the original question? Orig. ?: How many adults and children? Answer: 4 Adults and 16 Children A bunch of families are going to the movies. There are 20 people total. An adult ticket costs $10 and a child ticket costs $5. The total bill is $120. How many adults and how many children go to the movie?

6. System of Equations WORD PROBLEMS Name Apr 11, 2011 3. Example 2 1.What are you trying to find? How many messages for both plans to cost the same? 2.What do you know? Given in the problem? 2 plans: $40 plus $0.30 per message $60 plus $0.10 per message You are choosing a cell phone plan. One plan costs $40/month plus $0.30 for each text message. The other plan costs $60/month plus $0.10 for each text message. How many messages do you need to send for both plans to cost the same?

7. System of Equations WORD PROBLEMS Name Apr 11, 2011 From formulas and prior knowledge? Let C = cost and M = # messages sent We can setup a system of equations 3. How will you solve the problem? Eqn 1: Plan 1: C = 40 + 0.30M Eqn 2: Plan 2: C = 60 + 0.10M Both Slope-Intercept Form, so set them equal 3. Example 2 You are choosing a cell phone plan. One plan costs $40/month plus $0.30 for each text message. The other plan costs $60/month plus $0.10 for each text message. How many messages do you need to send for both plans to cost the same?

8. System of Equations WORD PROBLEMS Name Apr 11, 2011 3. How will you solve the problem? Eqn 1: Plan 1: C = 40 + 0.30M Eqn 2: Plan 2: C = 60 + 0.10M 40 + 0.30M = 60 + 0.10M - 0.10M - 0.10M 40 + 0.20M = 60 -40 0.20M = 20C = 40+ 0.30M M = 100C = 40+0.30(100) C = 70 3. Example 2 You are choosing a cell phone plan. One plan costs $40/month plus $0.30 for each text message. The other plan costs $60/month plus $0.10 for each text message. How many messages do you need to send for both plans to cost the same?

9. System of Equations WORD PROBLEMS Name Apr 11, 2011 4. Did you answer the original question? Orig. ?: How many messages for both plans to cost the same? Answer: 100 messages C = 40 + 0.30(100) = $70 C = 60 + 0.10(100) = $70 3. Example 2 You are choosing a cell phone plan. One plan costs $40/month plus $0.30 for each text message. The other plan costs $60/month plus $0.10 for each text message. How many messages do you need to send for both plans to cost the same? 100 messages is called the “break-even” point as it is the number of messages needed for the plans to cost the same. Neither plan is better than the other at that point

10. System of Equations WORD PROBLEMS Name Apr 11, 2011 4. Example 3 1.What are you trying to find? The cost of one bag of chips and one soda 2.What do you know? Given in the problem? 1 bag of chips + 1 soda costs $2.00 3 bags of chips + 2 sodas costs $4.75 One bag of chips and one soda costs $2.00. 3 bags of chips and two sodas costs $4.75. Ignore taxes. How much does one bag of chips cost? How much does one soda cost?

11. System of Equations WORD PROBLEMS Name Apr 11, 2011 From formulas and prior knowledge? Let C = cost of chips and S = cost of sodas (these are unknown) We can setup a system of equations 3. How will you solve the problem? Eqn 1: First deal: 1C + 1S = 2.00 Eqn 2: Second deal: 3C + 2C = 4.75 We need to adjust the first equation: -3(1C + 1S = 2.00) -3C – 3S = -6.00 4. Example 3 One bag of chips and one soda costs $2.00. 3 bags of chips and two sodas costs $4.75. Ignore taxes. How much does one bag of chips cost? How much does one soda cost?

12. System of Equations WORD PROBLEMS Name Apr 11, 2011 3. How will you solve the problem? Eqn 1: First deal: 1C + 1S = 2.00 Eqn 2: Second deal: 3C + 2C = 4.75 -3C – 3S = -6.00 3C + 2S = 4.75 - S = -1.25 S = 1.25 1C + 1(1.25) = 2.00 1C + 1.25 = 2.00 C = 0.75 4. Example 3 One bag of chips and one soda costs $2.00. 3 bags of chips and two sodas costs $4.75. Ignore taxes. How much does one bag of chips cost? How much does one soda cost?

13. System of Equations WORD PROBLEMS Name Apr 11, 2011 4. Did you answer the original question? Orig. ?: How much does one bag of chips cost? One soda cost? Answer: C = $0.75; bag of chips costs $0.75 S = $1.25; soda costs $1.25 1(0.75) + 1(1.25) = 2.00 3(0.75) + 2(1.25) = 4.75 4. Example 3 One bag of chips and one soda costs $2.00. 3 bags of chips and two sodas costs $4.75. Ignore taxes. How much does one bag of chips cost? How much does one soda cost?