1 / 19

CHAPTER 6

CHAPTER 6. Algebra: Equations and Inequalities. 6.3. Applications of Linear Equations. Objectives Use linear equations to solve problems. Solve a formula for a variable. Strategy for Solving Word Problems.

fspencer
Download Presentation

CHAPTER 6

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. CHAPTER 6 Algebra: Equations and Inequalities

  2. 6.3 • Applications of Linear Equations

  3. Objectives Use linear equations to solve problems. Solve a formula for a variable.

  4. Strategy for Solving Word Problems • Step 1 Read the problem carefully several times until you can state in your own words what is given and what the problem is looking for. Let x (or any variable) represent one of the quantities in the problem. • Step 2 If necessary, write expressions for any other unknown quantities in the problem in terms of x. • Step 3 Write an equation in x that models the verbal conditions of the problem. • Step 4 Solve the equation and answer the problem’s question. • Step 5 Check the solution in the original wording of the problem, not in the equation obtained from the words.

  5. Algebraic Translations of English Phrases

  6. Example: Education Pays Off • The bar graph shows the ten most popular college majors with median, or middlemost, starting salaries for recent college graduates.

  7. Example: Education Pays Off • The median starting salary of a business major exceeds that of a psychology major by $8 thousand. The median starting salary of an English major exceeds that of a psychology major by $3 thousand. Combined, their median starting salaries are $116 thousand. Determine the median starting salaries of psychology majors, business majors, and English majors with bachelor’s degrees.

  8. Example 1: continued • Step 1 Let x represent one of the unknown quantities. We know something about the median starting salaries of business majors and English majors: • Business majors earn $8 thousand more than psychology majors and English majors earn $3 thousand more than psychology majors. We will let • x = the median starting salary, in thousands of dollars, of psychology majors. • x + 8 = the median starting salary, in thousands of dollars, of business majors. • x + 3 = the median starting salary, in thousands of dollars, of English majors.

  9. Example: continued • Step 3: Write an equation in x that models the conditions. • x + (x + 8) + (x + 3) = 116 • Step 4: Solve the equation and answer the question.

  10. Example: continued • starting salary of psychology majors: x = 35 • starting salary of business majors: x + 8 = 35 + 8 = 43 • starting salary of English majors: x + 3 = 35 + 3 = 38. • Step 5: Check the proposed solution in the wording of the problem. The solution checks.

  11. Example: Selecting Monthly Text Message Plan • You are choosing between two texting plans. Plan A has a monthly fee of $20.00 with a charge of $0.05 per text. Plan B has a monthly fee of $5.00 with a charge of $0.10 per text. Both plans include photo and video texts. For how many text messages will the costs for the two plans be the same? • Step 1 Let x represent one of the unknown quantities. • Let x the number of text messages for which the two plans cost the same.

  12. Example: continued • Step 2 Represent other unknown quantities in terms of x. • There are no other unknown quantities, so we can skip this step. • Step 3 Write an equation in x that models the conditions. • The monthly cost for plan A is the monthly fee, $20.00, plus the per-text charge, $0.05, times the number of text messages, x. The monthly cost for plan B is the monthly fee, $5.00, plus the per-text charge, $0.10, times the number of text messages, x.

  13. Example: continued • Step 4 Solve the equation and answer the question. • Because x represents the number of text messages for which the two plans cost the same, the costs will be the same for 300 texts per month.

  14. Example: continued • Step 5 Check the proposed solution in the original wording of the problem. • Cost for plan A = $20 + $0.05(300) = $20 + $15 = $35 • Cost for plan B = $5 + $0.10(300) = $5 + $30 = $35. • With 300 text messages, both plans cost $35 for the month. Thus, the proposed solution, 300 text messages, satisfies the problem’s conditions.

  15. Example: A Price Reduction on a Digital Camera • Your local computer store is having a terrific sale on digital cameras. After a 40% price reduction, you purchase a digital camera for $276. What was the camera’s price before the reduction? • Step 1 Let x represent one of the unknown quantities. We will let x = the original price of the digital camera prior to the reduction. • Step 2 Represent other unknown quantities in terms of x. There are no other unknown quantities to find, so we can skip this step.

  16. Example: continued • Step 3 Write an equation in x that models the conditions. • The camera’s original price minus the 40% reduction is the reduced price, $276. • x − 0.4x = 276 • Step 4 Solve the equation and answer the question. • x − 0.4x = 276 • 0.6x = 276 x = 460 The camera’s price before the reduction was $460.

  17. Example: continued • Step 5 Check the proposed solution in the original wording of the problem. • The price before the reduction, $460, minus the 40% reduction should equal the reduced price given in the original wording, $276: • 460 − 40% of 460 = 460 − 0.4(460) = 460 − 184 = 276. • This verifies that the digital camera’s price before the reduction was $460.

  18. Example: Solving a Formula for a Variable • Solve the formula P = 2l + 2w for l. • First, isolate 2l on the right by subtracting 2w from both sides. Then solve for l by dividing both sides by 2. • P = 2l + 2w • P− 2w = 2l + 2w− 2w • P − 2w = 2l

  19. The total price of an article purchased on a monthly deferred payment plan is described by the following formula: T is the total price, D is the down payment, p is the monthly payment, and m is the number of months one pays. Solve the formula for p. T – D = D – D + pm T – D = pm T – D = pm m m T – D = p m Example: Solving a Formula for One of its Variables

More Related