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SYSTEMS OF EQUATIONS

SYSTEMS OF EQUATIONS. AGE PROBLEMS. WARM UP. Dominique paints faces at an annual carnival. Her goal this year is to earn $100. She spends $15 on supplies and will work for 2.5 hours. How much will she need to earn in dollars per hour in order to reach her goal? Solve ax + bx = c for x.

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SYSTEMS OF EQUATIONS

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  1. SYSTEMS OF EQUATIONS AGE PROBLEMS

  2. WARM UP Dominique paints faces at an annual carnival. Her goal this year is to earn $100. She spends $15 on supplies and will work for 2.5 hours. How much will she need to earn in dollars per hour in order to reach her goal? Solve ax + bx = c for x. Find the range of the function with domain {-2, 0, 3.5}: f(x) = - 2x² The owner of a hair salon charges $20 more per haircut than the assistant. Yesterday the assistant gave 12 haircuts. The owner gave 6 haircuts. The total earnings from haircuts were $750. How much does the owner charge for a haircut?

  3. AGE To represent a past age, subtract from the present age. To represent a future age, add to the present age.

  4. Bill is three times as old as Sara. Six years from now, Bill will be twice as old as Sara will be then. Find the present age of both Bill and Sara.

  5. Bill is three times as old as Sara. Six years from now, Bill will be twice as old as Sara will be then. Find the present age of both Bill and Sara. Let x = Sara’s age x + 6 = Sara’s age 6 years from now. Let 3x = Bill’s age 3x + 6 = Bill’s age 6 years from now. 3x + 6 = 2(x + 6) 3x + 6 = 2x + 12 3x – 2x = 12 – 6 x = 6 (Sara) Bill = 18

  6. John is now 4 times as old as his brother Sam. In 4 years, John will be twice as old as Sam will be then. Find their present ages. John: _______________ Brother: _____________

  7. A father is three times as old as his son. Fifteen years ago, the father was 9 times as old as his son was then. Find their present ages. Father: ________________ Son: __________________

  8. Helen is now 20 and Arlene is now 10 years old. How many years ago was Helen three times as old as Arlene was then? Helen: ______________ Arlene: _____________

  9. Andy is twice as old as Kate. In 6 years, their ages will total 60. How old is each now? Andy: _____________ Kate: ______________

  10. Mr. Wilson is 15 years older than Mr. Connors. Five years from now, Mr. Wilson will be 1½ times as old as Mr. Connors will be then. How old is each man now? Mr. Wilson: ________________ Mr. Connors: ________________

  11. Phil is 24 years older than Stanley. Four years ago, he was 7 times as old as Stanley was then. Find their present ages.

  12. A realtor has two homes for sale. Ten years ago the older home was four times as old as was the newer home. Thirty years from now, the older home will be twice as old as the newer home will be. How old are the homes now? Older home: _________________ Newer home: ________________

  13. The sum of a man’s age and his daughter’s age is 50 years. Eight years from now, the man will be twice as old as his daughter will be then. Find the present age of each. Father’s age: ______________________ Daughter’s age: ___________________

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