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Warm Up

Warm Up. Write an expression for: one less than twice a number. Use n to represent the number. Simplify. Use positive exponents. . Warm Up. 1.Write an expression for: one less than twice a number. Use n to represent the number. 2n-1 2. Simplify. Use positive exponents. .

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Warm Up

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  1. Warm Up • Write an expression for: one less than twice a number. Use n to represent the number. • Simplify. Use positive exponents.

  2. Warm Up 1.Write an expression for: one less than twice a number. Use n to represent the number.2n-1 2. Simplify. Use positive exponents.

  3. Using Systems to Solve Problems (day 3 of 3) MCC9-12.A.REI.5 & MCC9-12.A.REI6 Learning Target: I am learning to write and solve a system of equations to answer real world problems. In unit 1, you wrote and solved equations with one variable. In this lesson, we will write and solve a system of 2 equations using 2 different variables to answer a real world problem.

  4. To solve a word problem by using a system of 2 equations with 2 variables: • 1. Decide what 2 quantities you need to find and choose 2 variables to represent them. (This is referred to as “defining your variables”.) • 2. Use the information given in the problem to write two equations which show the relationships between the quantities. • 3. Solve the system ( use substitution, elimination, or graphing). • 4. Interpret the solution to answer the problem. • 5. Check your answer in the original question.

  5. Ex. 1 When Angelo cashed a check for $170, the bank teller gave him 12 bills, some $20s and the rest $10s. How many of each denomination did Angelo receive? We need to determine how many $20 bills and how many $10 bills he received Define variables: x=____________________ y=____________________ Use the total number of bills to write one equation: ______+______=________ (total tells us to add) Use the value to write another equation: ________+________=_________

  6. Solve the system: Interpret your solution, and check in the original problem.

  7. Ex. 2: A rectangle has a perimeter of 38ft. The length is 1ft less than 3 times the width. Find the dimensions of the rectangle. Define variables: ____________ _____________ Write an equation that relates the length and the width. _______________________ Recall the formula for the perimeter of a rectangle(or just add all the sides) to write an equation. _______________________________________ or_____________________________________

  8. Solve the system. Interpret your solution to answer the question, and check your answer.

  9. Ex. 3. Mr. Stamos invested a sum of money in CDs earning 4% a year and another sum of money in bonds earning 6% a year. The total he invested was $4000. If his combined interest earned for the year was $188, how much did he invest in each?

  10. Ex. 4 Tickets for a dance cost $10 in advance and $15 at the door. If 100 tickets were sold and $1200 was collected, how many tickets were sold in advance and how many were sold at the door?

  11. Ex. 5. Carmen walks at a rate of 2 mph and jogs at a rate of 4mph. she walked and jogged a total of 3.4 miles in 1.2 hours. For how long did Carmen jog, and for how long did she walk?

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