Bellwork 1. A salesman's salary is $18,500 per year. In addition, the salesman earns 5% commission on the year's sales. Last year the salesman earned $25,400. How much was sold that year? 2. The area of a rectangle is A = l ∙ w. If the length of the rectangle is l = w + 4, write A in terms of l only. X = the amount of sales last year 18, x = 25, x = 6900 X = $138,000 W = l – 4 A = l (l – 4) A = l 2 – 4l

Check 1.4 HW

Section 1. 5: Word Problems Read and understand the problem Devise a plan Carry out Plan Look Back Always Define Your Variables!

1. The perimeter of a parallelogram is 52 cm. What is the length of the longer side if the shorter side measures 10 cm? X= the length of the longer side P = 2l + 2w 52 = 2x + 2(10) 52 = 2x = 2x 16 = x

2. The length of a rectangle is 4 feet more than twice the width. The perimeter is 116. Find the dimensions of the rectangle. X= width 2X + 4 = length P = 2l + 2w 116 = 2(2x+4) + 2(x) 116 = 4x x 116 = 6x = 6x 18 = x Width = 18 Length = 2(18) + 4 = 40

3. On Tuesday, Ed's sports store sold twice as many T- shirts as shorts. T-shirts are $9 each and shorts are $14 each. The total amount of money taken in for both items was $256. Find the number of each that was sold. X = # of shorts 2x = # of t-shirts 14(x) + 9(2x) = x + 18x = x = 256 X = 8 8 pairs of shorts and 2(8) or 16 t-shirts

4. Alan bought 5 lbs of peanuts for $2.50 per pound. He also bought cashews for $6 per pound. If Alan spent $30.50, how many pounds of cashews did he buy? X = # of pounds of cashews 5(2.50) + x(6) = x = X = 18 X = 3 3 pounds of cashews

5. Abe is 3 years older than Mindy. The sum of their ages is 39. What are their ages? X = Mindy's age X + 3 = Abe's age X + (x + 3) = 39 2X + 3 = 39 2X = 36 X = 18 X + 3 = = 21 Mindy is 18 and Abe is 21

6. Sara is 10 years younger than her sister. Six years from now the sum of their ages will be 76. How old are Sara and her sister now? X = sara's age now X + 10 = sister's age now X + 6 = sara's age in six years X = sister's age in six years (X + 6)+ (x ) = 76 2X + 22 = 76 2X = 54 X = 27 X + 10 = = 37 Sara is 27 and her sister is 37

7. Eugene has 5 more dimes than nickels. In all he has $2.30. How many nickels and dimes does Eugene have? X = the number of nickels X + 5 = dimes.05x +.10(x + 5) = x +.10x +.5 = x = 1.80 X = 12 X + 5 = = nickels and 17 dimes

8. Sue sold a total of 105 tickets at the ball game. Each adult ticket cost $2.50 and each student ticket cost $1.10. The total income was $ How many of each kind of ticket were sold? X = # of adult tickets 105 – x = # of student ticket 2.50(x) (105 – x) = x – 1.10x = x = x = 86.8 X = – x = 105 – 62 = adults and 43 students

9. Bob's dad is 27 years older than Bob. The sum of their ages 5 years ago was 45. How old is Bob now? X = Bob's age now X + 27 = Dad's age now X – 5 = Bob's age five years ago X + 27 – 5 = Dad's age five years age (x – 5) + (x + 27 – 5) = 45 2X + 17 = 45 2X = 28 X = 14 X + 27 = = 41 Bob is 14 and his Dad is 41

10. The Bullet Train runs between the Japanese cities of Osaka and Fukuoka, a distance of 550 kilometers. When it makes no stops, it takes 2 hours and 15 minutes to make the trip. What is the average speed of the Bullet Train? D = r x t 550 = r x 2 15/ = 2.25r 2200=r

15. The sum of two consecutive integers is 131. Find the integers. X= first integer X + 1 second integer X + (x + 1) = 131 2x + 1 = 131 2x = 130 X = 65 X + 1 = = 66

16. The sum of the least and greatest of three consecutive integers is sixty. Find the three integers. X = the first integer X + 1 = the second integer X + 2 = the third integer X + (x + 2) = 60 2X + 2 = 60 2X = 58 X = 29 X + 1 = = 30 X + 2 = = 31 29, 30, and 31

17. The lengths of the sides of a triangle are consecutive odd integers. What is the length of the longest side if the perimeter of the triangle is 45? X = the first side X + 2 = the second side X + 4 = the third side X + (x + 2) + (x + 4) = 45 3X + 6 = 45 3X = 39 X = 13 X + 2 = = 15 X + 4 = = 17 13, 15, and 17

18. John has a board that is 5 feet long. He plans to make four shelves whose lengths are a series of consecutive even integers. How long should each board be in inches? X = first shelf X + 2 = second shelf X + 4 = third shelf X + 6 = fourth shelf X + (x+ 2) + (x + 4) + (x + 6) = 60 *5 feet = 60 inches 4X + 12 = 60 4X = 48 X = 12 X + 2 = = 14 X + 4 = = 16 X + 6 = = 18 12, 14, 16, 18

19. Find three consecutive odd integers such that the sum of the first and second is 31 less that 3 times the third. X = 1 st integer X + 2 = 2 nd integer X + 4 = 3 rd integer X + (x + 2) = 3(x+ 4) – 31 2X + 2 = 3x + 12 – 31 2X + 2 = 3x – 19 – x = – 21 X = 21 X + 2 = = 23 X + 4 = = 25 21, 23, 25

20. The sum of two numbers is 57. If the larger of the two numbers is 9 less than twice the smaller, find the two numbers. X = smaller # 2x – 9 = larger # X + (2x – 9) = 57 3X – 9 = 57 3X = 66 X = 22 2x – 9 = 2(22) – 9 = and 35

Jim has $4.05 in nickels and dimes. He has 6 more dimes than nickels. How many of each coin does he have? Closure X = # of nickels X + 6 = # of dimes.05(x) +.10(x + 6) = x +.10x +.6 = x = 3.45 X = 23 X + 6 = = nickels and 29 dimes