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Math Session 5

Word Problems on

Integers, Fractions, Rational Exponents, Motion, Mixture, Money, Geometry

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- 1. WORD PROBLEMS TIU College Entrance Test Review Math Session 5
- 2. PRB / Fractions Example (Not in the book) <ul><li>3 Methods: </li></ul><ul><li>By drawing </li></ul><ul><li>By PRB method (Percentage-Rate-Base) </li></ul><ul><li>By Algebra </li></ul>
- 3. Method 2: PRB triangle
- 4. Method 3: By Algebra
- 5. Fractions Example 2 (Not in the book) <ul><li>Answer: 16 . </li></ul>
- 6. Defined Operations (Example not in the book) <ul><li>The word problem will use a symbol / character to define an operation / process. </li></ul>What to do: Use the given formula in the problem to solve.
- 7. Rational Exponents / Radicals (This example not in the book) <ul><li>RECALL: </li></ul>YES!
- 8. Just getting the cube root.
- 10. p.76 Ex. 3 NUMBER PROBLEM <ul><li>The sum of three consecutive even integers is 66. What is the largest number? </li></ul>The largest is 24.
- 11. Ex. 21 p. 83 Motion Problem <ul><li>Ross and Rachel agree to meet for a date. Ross drives at 40 kph and Rachel at 35 kph. After how many hours will they meet if they are 150 km apart and they start driving directly toward each other at the same time? </li></ul>1.) Make a diagram/illustration of the scene. 2.) Make a table of the given.
- 12. Let t = number of hours until they meet = time Ross traveled = time Rachel Diagram Ross, 40kph Rachel, 35 kph 150 km We use the formula, distance = rate x time
- 13. p. 87 Ex. 29 MIXTURE How much water must be added to 100 L of denatured alcohol 90% pure to dilute into 75% alcohol content? 100 L 90 % X 0% 100 + X 75%
- 14. p. 88 Ex. 32 MONEY <ul><li>A scholarship trust fund has P65,000 in capital. Some of the money is invested in a bank at an annual interest rate of </li></ul><ul><li>and the rest at 6%. If the </li></ul><ul><li>income from the amount invested at </li></ul><ul><li>exceeds the investment at 6% by P300 after one year, how much is invested at each rate? </li></ul>
- 15. Money P65,000 6% Interest at 4.5% = 4.5%x Interest at 6% = 6% (65,000 – x) Let x = money invested at 4.5% Equation?
- 16. p. 88 Ex. 32 MONEY <ul><li>A scholarship trust fund has P65,000 in capital. Some of the money is invested in a bank at an annual interest rate of </li></ul><ul><li>and the rest at 6%. If the </li></ul><ul><li>income from the amount invested at </li></ul><ul><li>exceeds the investment at 6% by P300 after one year, how much is invested at each rate? </li></ul>
- 17. “… income from the amount invested at exceeds the investment at 6% by P300 after one year.” <ul><li>. </li></ul>Interest at 4.5% : 4.5%x Interest at 6% : 6% (65,000 – x) Note: If time is more than one year or investment period:
- 18. Geometry Example 1 (Not in the book) <ul><li>The edge of a cube is doubled. What happens to its volume? </li></ul>Volume increases 8 times bigger.
- 19. GEOMETRY Example (Not in the book) An architect is to design a swimming pool in a hotel, to be fenced off on 3 sides with 60 meters of material. The pool is to have an area of 352 sq.m. What should the dimensions of the pool be? L W
- 20. System of Equations: Perimeter Area <ul><li>Let’s use SUBSTITUTION METHOD: </li></ul><ul><li>Represent L in terms of W. </li></ul><ul><li>Substitute into 2 nd equation. </li></ul>
- 21. Can we isolate the variable W above? The equation above is NOT linear. It is A QUADRATIC equation. (Degree of x is 2) How can we solve for W?
- 22. Page 60 3 Methods to solve Quadratic Equations: <ul><li>1.) FACTORING </li></ul><ul><li>2.) COMPLETING THE SQUARE </li></ul><ul><li>3.) QUADRATIC FORMULA </li></ul>
- 23. Factoring

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