Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Page 1 Chapter 9 Word Problems Basic Word Problems Introduction Word problems come in several types. You will find several basic types of word problems in every algebra book. Each different type has a slightly different set up but they all have many things in common. Many of these basic types are not exactly like the word problems you will encounter in nursing, electronics, business or even in your daily life. The basic types of word problems that we use in this chapter have been selected to help teach you the basic procedures and concepts which can be used in almost all word problems you may encounter in other areas of study. If you master these you will often be able to solve other problems that differ from the types you have learned in this course. This unit will show you step by step what to do to set up and solve the types of word problems that we will cover. How do you start to set up a word problem? 1. Read the problem all the way through once to see what type of problem it is. 2. Determine the two (or three) unknown quantities that you are being asked to find the values for. Look for a sentence that asks you to find something or for a sentence with a question mark ? 3. Look for a sentence that compares the first two unknowns. The sentence that does this will state things like “the numbers of dogs is 5 more than the number of cats” 4. Start the problem with Let “something” = x. We let x equal the quantity that is being used as the basis for comparison. The quantity mentioned second in the sentence is almost always the quantity the other quantities are compared to. This means that the quantity mentioned second is set equal to x and the first quantity will be an expression with x in it. 4. Express the second unknown as a statement with the unknown written in terms of x by using the translations on the next page. 5. Go back and read the problem again. A second sentence will help you set up an equation. It is very common for that sentence to state what the total value of the unknowns is. 6. Solve the equation for the unknown variable. 7. Plug the value of x into the expression for the other unknowns to find their values. 8. State the solution by listing each unknown and its value. 9. Check your solution in the original problem to see if the solution works. Chapter 9 © 2015 Eitel Translating Word Problems How to translate English Statements into Algebraic Expressions Listed below are examples of some of the most common statements found in word problems. Each English statement has been translated into an algebra statement with x as the unknown. You should study the order of the unknown term and the constant term. It is a common mistake to reverse the order. English Statement Algebra Expression is, was, will be = times, of, product multiply twice a number or two times a number * 2x three times a number * 3x four times a number * 4x more than, increased by, sum add 6 more than a number * x+6 (6 added at the end) 7 more than twice a number * 2x + 7 (7 added at the end) 4 more than 3 times a number * a number increased by 10 the sum of a number and 7 3x + 4 x + 10 x+7 (4 added at the end) less than, decreased by subtract: order is very important 5 less than a number * x–5 (5 subtracted at the end) 2x – 4 (4 subtracted at the end) 7 less than three times a number 3x – 7 (7 subtracted at the end) (4 subtracted at the end) a number decreased by 10 2x – 8 x – 10 4 less than twice a number * * 8 less than two times a number * Ratio (quotient) the ratio of Doctors to Nurses division D N the ratio of Cars to Trucks C T the ratio of Miles to Gallons M G Chapter 9 © 2015 Eitel Page 3 Translation Problems Translate each English expression into an algebraic expression. English Algebra English Algebra 1. 5 more than a number _________ 16. 12 less than 5 times a number _________ 2. 5 times a number _________ 17. 2 less than 3 times a number _________ 3. 1 more than a number _________ 18. 4 more than 5 times a number _________ 4. 12 less than a number _________ 19. 1 more than twice a number _________ 5. 3 times a number _________ 20. 6 less than 7 times a number _________ 6. 7 more than a number _________ 21. 3 more than twice a number _________ 7. 8 less than a number _________ 22. 9 more than 3 times a number _________ 8. 4 times a number _________ 23. 12 less than 3 times a number _________ 9. 10 less than a number _________ 24. 9 less than 6 times a number _________ 10. twice a number _________ 25. 6 more than 5 times a number _________ 11. 8 times a number _________ 26. 1 more than 4 times a number _________ 12. 12 more than a number _________ 27. _________ 13. 20 less than a number _________ 28. 5 less than twice a number _________ 14. 15 more than a number _________ 29. 7 more than twice a number _________ 15. _________ 30. 4 less than 7 times a number _________ 5 less than a number Chapter 9 9 more than 6 times a number © 2015 Eitel 9 – 3 Answers 1. x + 5 7. x – 8 13. x – 20 19. 2x + 1 25. 5x + 6 Chapter 9 2. 5x 8. 4x 14. x + 15 20. 7x – 6 26. 4x + 1 3. x + 1 9. x – 10 15. x – 5 21. 2x + 3 27. 6x + 9 4. x – 12 10. 2x 16. 5x – 12 22. 3x + 9 28. 2x – 5 5. 3x 11. 8x 17. 3x – 2 23. 3x – 12 29. 2x + 7 6. x + 7 12. x + 12 18. 5x + 4 24. 6x – 9 30. 7x – 4 © 2015 Eitel