1. S OLVING W ORD P ROBLEMS Using Algebraic Equations

2. T RANSLATIONS plus/ add subtract /minus greater thandifference /less than increase / largernegative / decrease augment / sum reduce / diminish times / of quotient multiply divided by product a number of parts

3. T RANSLATIONS equal / equal to / is / results in gives you / makes / quotient / sum difference / product a number / an age / a quantity a distance / a width / a height a mass / a volume / a price / a length an amount / a number of coins

4. E NGLISH P HRASES

5. C REATE A LGEBRAIC E QUATIONS

6. N EW L ANGUAGE Consecutive Integers: Consecutive Even Integers: Consecutive Odd Integers: Complementary Angles: Supplementary Angles:

7. N UMBER P ROBLEMS - N OTES 1. Identify what you are looking for and call it ‘x’. 2. Translate the problem into a mathematical statement (equation). 3. Solve the equation for ‘x’. 4. Use this knowledge of ‘x’ to answer the question. Use a final statement.

8. N UMBER P ROBLEMS - E XAMPLE 1 If a number is tripled and the result increased by four, the sum is sixty-four. Find the number. Number = x Equation 3x + 4 = 64 Solve 3x = 64 – 4 3x = 60 x = 60/3 x = 20 Solution – the number is 20.

9. N UMBER P ROBLEMS - E XAMPLE 2 The larger of two numbers is seven more than five times the smaller number. If their sum is sixty-one, what are the numbers? Larger Number = 5x +7Smaller Number = x Equation 5x + 7 + x = 61 Solve 6x +7 = 61 6x = 61 – 7 6x = 54 x = 54/6 x = 9 Solution – the small number is 9 and the larger is 5(9) + 7 = 52.

10. N UMBER P ROBLEMS - E XAMPLE 3 The sum of three consecutive numbers is seventy- eight. What are the numbers? First : xSecond: x + 1Third: x +2 Equationx + x + 1 + x + 2 = 78 Solve 3x + 3 = 78 3x = 78 – 3 3x = 75 x = 75/3 x = 25 Solution – The consecutive numbers are 25, 26, and 27.

11. N UMBER P ROBLEMS - E XAMPLE 4 If three is added to a number and the sum is multiplied by two, the result is the same as nine subtracted from three times the number. Find the number. Number = x Equation2(x + 3) = 3x – 9 Solve2x + 6 = 3x – 9 2x – 3x = -9 – 6 - x = - 15 x = 15 Solution - The number is 15.

12. P RACTICE P ROBLEMS Do questions 1- 12 on loose leaf. You DO NOT need to copy the question, but follow the sequence to solve. Do only questions 1-6 for modified students. Check answers at the back.

13. G EOMETRIC P ROBLEMS - N OTES 1. Identify what you are looking for and call it ‘x’ or another variable. 2. Use a diagram and label parts that you know, including your variable that you don’t know. 3. Translate the problem into a mathematical statement (equation). 4. Solve the equation for your variable. 5. Answer the question. Use a final statement. Some equations are given on your sheet.

14. G EOMETRIC P ROBLEMS - E XAMPLE 1 If the two equal sides of an isosceles triangle are each five times as long as the base, and the perimeter is 253 metres, find the length of each side. Base = xSide 1 = 5xSide 2 = 5x Equationx + 5x + 5x = 253 Solution: the base is 23m, and each of the sides are 5x23=115m. 5x x

15. G EOMETRIC P ROBLEMS - E XAMPLE 2 Two angles of a triangle are congruent. The third is twice as large as either of the other two What is the measure of each angle? (Remember – angles of a triangle add to 180°) <1 = x <2 = x < 3= 2x Equationx + x + 2x = 180 Solution: two angles are 45°. And the other angle is 2(45) = 90°. 2x xx

16. G EOMETRIC P ROBLEMS - E XAMPLE 3 A farmer uses 54 hectometers of fencing to enclose a rectangular field. If the width is two hectometers less than the width, find the dimensions of the field. Length = xWidth = x – 2 P = 54hm Equation2(x + x – 2) = 54 Solution: the length is 14.5 hm and the width is 14.5 – 2= 12.5hm. x - 2 x

17. A GE P ROBLEMS - N OTES 1. Identify the unknown and call it ‘x’ or another variable. 2. Use a chart to organize your information – including ages now, in the past and in the future. 3. Translate the problem into a mathematical statement (equation). 4. Solve the equation for your variable. 5. Answer the question. Use a final statement.

18. A GE P ROBLEMS - E XAMPLE 1 A father is now only three times as old as his son. Either years ago the father was five times as old as his son. Find their present ages. Equation 3x – 8 = 5(x-8) Solution:.The son is 16 and the father is 3(16) = 48. FatherSon Now3xx Past3x – 8x – 8

19. A GE P ROBLEMS - E XAMPLE 2 John is twice as old as Bill. In five years, the sum of their ages will be thirty-four. Equation 2x + 5 + x + 5 = 34 Solution:. Bill is 8 years old now, and John is 2(8) = 16 years old. JohnBill Now2xx Future2x + 5x + 5

20. A GE P ROBLEMS - E XAMPLE 3 A mother is three years less than five times as old as her daughter. If the sum of their ages is thirty-nine, find the age of each. Equation 5x – 3 + x = 39 Solution:. The daughter is 7 years old and the mother is 5(7)-3 = 32 years old. MotherDaughter Now5x – 3x