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1. Problem Solving Steps. 1. ALWAYS use these steps when solving word problems:. What are you trying to find? 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?. 2. Example 1. 2.

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  1. 1. Problem Solving Steps 1. ALWAYS use these steps when solving word problems: • What are you trying to find? • 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?

  2. 2. Example 1 2. 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? • What are you trying to find? • The number of adults and children • 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

  3. 2. Example 1 2. 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? • 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

  4. 2. Example 1 2. 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. 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 Adults A = 4 16 Children 4 + C = 20 C = 16

  5. 2. Example 1 2. 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. Did you answer the original question? Orig. ?: How many adults and children? Answer: 4 Adults and 16 Children

  6. 3. Example 2 3. 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? • What are you trying to find? • How many messages for both plans to cost the same? • What do you know? • Given in the problem? • 2 plans: $40 plus $0.30 per message • $60 plus $0.10 per message

  7. 3. Example 2 3. 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? • 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

  8. 3. Example 2 3. 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? 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 -40 0.20M = 20 C = 40 + 0.30M M = 100 C = 40+0.30(100) C = 70

  9. 3. Example 2 3. 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 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

  10. 4. Example 3 4. 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? • What are you trying to find? • The cost of one bag of chips and one soda • 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

  11. 4. Example 3 4. 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? • 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

  12. 4. Example 3 4. 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? 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

  13. 4. Example 3 4. 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? 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

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