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Warm Up

Warm Up. Two planes, which are 2400 miles apart, fly toward each other. Their speeds differ by 60 miles per hour. They pass each other after 5 hours. Find their speeds. x=speed of slower plane x=210. Standards.

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Warm Up

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  1. Warm Up • Two planes, which are 2400 miles apart, fly toward each other. Their speeds differ by 60 miles per hour. They pass each other after 5 hours. Find their speeds. • x=speed of slower plane • x=210

  2. Standards • MCC9-12.A.REI.5 Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions. • MCC9-12.A.REI.6 Solve systems of linear equations exactly and approximately (IE with graphs), focusing on pairs of linear equations in two variables.

  3. What about those with multiple variables? • The sum of two numbers is 24. The difference of the two numbers is 6. Find the two numbers. • a+b=24 • a-b=6

  4. 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?

  5. 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.

  6. 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?

  7. 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?

  8. Carmen walks at a rate of 2mph 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?

  9. A test has twenty questions worth 100 points. The test consists of True/False questions worth 3 points each and multiple choice questions worth 11 points each. How many multiple choice questions are on the test? • x + y = 20 • 3x + 11y = 100

  10. Margie is responsible for buying a week's supply of food for the dogs and cats at a local shelter. The food for each dog costs twice as much as those supplies for a cat. She needs to feed 164 cats and 24 dogs. Her budget is $4240. How much can Margie spend on each dog for food? • d=2c • 164c + 24d = 4240

  11. Castel and Gabriella are selling pies for a school fundraiser. Customers can buy apple pies and lemon meringue pies. Castel sold 6 apple pies and 4 lemon meringue pies for a total of $80. Gabriella sold 6 apple pies and 5 lemon meringue pies for a total of $94. What is the cost each of one apple pie and one lemon meringue pie? • 6a + 4l = 80 • 6a + 5l = 94

  12. The sum of the digits of a two digit number is 6. When the digits are reversed, the number increases by 18. What is the number?

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