2.3 Applications. 9. Let w represent the width and 2w represent the length. Using the perimeter formula:

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1 2.3 Applications 1. Let w represent the width and 2w represent the length. Using the perimeter formula: 2w + 2 2w ( ) = 60 2w + 4w = 60 6w = 60 w = 10 The dimensions are 10 feet by 20 feet. 3. Let s represent the side of the square. Using the perimeter formula: 4s = 28 s = 7 The length of each side is 7 feet. 5. Let x represent the shortest side, x + 3 represent the medium side, and 2x represent the longest side. Using the perimeter formula: x + x x = 23 4x + 3 = 23 4x = 20 x = 5 The shortest side is 5 inches. 7. Let w represent the width and 2w 3 represent the length. Using the perimeter formula: 2w + 2 2w! 3 ( ) = 18 2w + 4w! 6 = 18 6w! 6 = 18 6w = 24 w = 4 The width is 4 meters. 9. Let w represent the width and 2w represent the length. Using the perimeter formula: 2w + 2 2w ( ) = 48 2w + 4w = 48 6w = 48 w = 8 The width is 8 feet and the length is 16 feet. Finding the cost: C = 1.75(32) (16) = = 92 The cost to build the pen is $92.00.

2 11. Let b represent the amount of money Shane had at the beginning of the trip. Using the percent increase: b b = b = 300 b = 200 Shane had $ at the beginning of the trip. 13. Let c represent the cost for the bookstore. Using the markup equation: c c = c = 115 c! The cost to the bookstore was approximately $ Let R represent the total box office receipts. The equation is: 0.53R = 52.8 R! 99.6 The total receipts were approximately $99.6 million. 17. Let x represent one angle and 8x represent the other angle. Since the angles are supplementary: x + 8x = 180 9x = 180 x = 20 The two angles are 20 and a. Let x represent one angle and 4x 12 represent the other angle. Since the angles are complementary: x + 4x! 12 = 90 5x! 12 = 90 5x = 102 x = 20.4 ( )! 12 = x! 12 = The two angles are 20.4 and b. Let x represent one angle and 4x 12 represent the other angle. Since the angles are supplementary: x + 4x! 12 = 180 5x! 12 = 180 5x = 192 x = 38.4 ( )! 12 = x! 12 = The two angles are 38.4 and

3 21. Let x represent the smallest angle, 3x represent the largest angle, and 3x 9 represent the third angle. The equation is: x + 3x + 3x! 9 = 180 7x! 9 = 180 7x = 189 x = 27 The three angles are 27, 72 and Let x represent the largest angle, 1 3 x represent the smallest angle, and 1 x + 10 represent the third 3 angle. The equation is: 1 3 x + x + 1 x + 10 = x + 10 = x = 170 x = 102 The three angles are 34, 44 and Let x represent the measure of the two base angles, and 2x + 8 represent the third angle. The equation is: x + x + 2x + 8 = 180 4x + 8 = 180 4x = 172 x = 43 The three angles are 43, 43 and Let h represent the height the ladder makes with the building. Using the Pythagorean theorem: h 2 = h 2 = 625 h 2 = 576 h = 24 The ladder reaches a height of 24 feet along the building.

4 29. Let x, x + 2, and x + 4 represent the three sides. Using the Pythagorean theorem: x 2 + x + 2 ( ) 2 = ( x + 4) 2 x 2 + x 2 + 4x + 4 = x 2 + 8x x 2 + 4x + 4 = x 2 + 8x + 16 x 2! 4x! 12 = 0 ( x! 6) ( x + 2) = 0 x = 6 (x =!2 is impossible) The lengths of the three sides are 6, 8, and Let w represent the width and 3w + 2 represent the length. Using the area formula: w 3w + 2 ( ) = 16 3w 2 + 2w = 16 3w 2 + 2w! 16 = 0 ( 3w + 8) ( w! 2) = 0 w = 2 (w =! 8 3 is impossible) The dimensions are 2 feet by 8 feet. 33. Let h represent the height and 4h + 2 represent the base. Using the area formula: 1 ( 2 4h + 2) ( h) = 36 4h 2 + 2h = 72 4h 2 + 2h! 72 = 0 ( ) = 0 2 2h 2 + h! 36 ( )( h! 4) = 0 2 2h + 9 h = 4 (h =! 9 2 is impossible) The base is 18 inches and the height is 4 inches.

5 35. Let x represent the amount invested at 8% and 9000 x represent the amount invested at 9%. The equation is: 0.08x ( 9000! x) = x + 810! 0.09x = 750!0.01x = 750!0.01x =!60 x = 6000 She invested $6,000 at 8% and $3,000 at 9%. 37. Let x represent the amount invested at 12% and x represent the amount invested at 10%. The equation is: 0.12x ( 15000! x) = x ! 0.10x = x = x = 100 x = 5000 The investment was $5,000 at 12% and $10,000 at 10%. 39. Let x represent the amount invested at 8% and 6000 x represent the amount invested at 9%. The equation is: 0.08x ( 6000! x) = x + 540! 0.09x = 500!0.01x = 500!0.01x =!40 x = 4000 Stacey invested $4,000 at 8% and $2,000 at 9%. 41. Let t represent the required time. Using the Pythagorean theorem: ( 15t) 2 + ( 20t) 2 = t t 2 = t 2 = t 2! 5625 = 0 625( t 2! 9) = 0 t =!3,3 Since the time must be positive, the time is 3 hours.

6 43. Completing the table: 45. Completing the table: Speed (miles per hour) Time (hours) Distance (miles) Distance Upstream (miles) Distance Downstream (miles) Let x represent the number of father tickets and 75 x represent the number of son tickets. The equation is: 2x ! x ( ) = x ! 1.5x = x = x = 15 x = 30 So 30 fathers and 45 sons attended the breakfast. 49. The total money collected is: $1204! $250 = $954 Let x represent the amount of her sales (not including tax). Since this amount includes the tax collected, the equation is: x x = x = 954 x = 900 Her sales were $900, so the sales tax is: 0.06(900) = $54

7 51. Let x represent the length of Patrick s call. He talks 1 minute at 40 cents and x 1 minutes at 30 cents, so the equation is: 40 1 ( ) + 30( x! 1) + 50 = x! = x + 60 = x = 1320 x = 44 Patrick talked for 44 minutes. 53. Completing the table: 55. Completing the table: 1 7 t h Year Sales (billions of dollars) Completing the table: 59. Completing the table: Age Maximum Heart Rate w l A (years) (beats per minute) Completing the table: Resting Heart Rate (beats per minute) Training Heart Rate (beats per minute)

8 63. Graphing the inequality: 65. Graphing the inequality: 67. Solving the equation: 69. Solving the equation:!2x! 3 = 7!2x = 10 x =!5 3( 2x! 4)! 7x =!3x 6x! 12! 7x =!3x! x! 12 =!3x!12 =!2x x = 6