Section_1.6-Modeling with Equations

Section_1.6-Modeling with Equations - Section 1.6 Modeling...

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Unformatted text preview: Section 1.6 Modeling with Equations EXAMPLE: A car rental company charges $30 a day and 15c a mile for renting a car. Helen rents a car for two days and her bill comes to $108. How many miles did she drive? Solution: We are asked to find the number of miles Helen has driven. So we let x = number of miles driven Then we translate all the information given in the problem into the language of algebra. Now we set up the model. milage cost + daily cost = total cost . 15 x + 2(30) = 108 . 15 x = 48 x = 48 . 15 x = 320 Helen drove her rental car 320 miles. 1 EXAMPLE: Mary inherits $100,000 and invests it in two certificates of deposit. One certificate pays 6% and the other pays 4 1 2 % simple interest annually. If Marys total interest is $5025 per year, how much money is invested at each rate? Solution: The problem asks for the amount she has invested at each rate. So we let x = the amount invested at 6% Since Marys total inheritance is $100,000, it follows that she invested 100 , 000- x at 4 1 2 % . We translate all the information given into the language of algebra. We use the fact that Marys total interest is $5025 to set up the model. interest at 6% + interest at 4 1 2 % = total interest . 06 x + 0 . 045(100 , 000- x ) = 5025 . 06 x + 4500- . 045 x = 5025 . 015 x + 4500 = 5025 . 015 x = 525 x = 525 . 015 = 35 , 000 So Mary has invested $35,000 at 6% and the remaining $65,000 at 4 1 2 % . EXAMPLE: A poster has a rectangular printed area 100 cm by 140 cm, and a blank strip of uniform width around the four edges. The perimeter of the poster is 1 1 2 times the perimeter of the printed area. What is the width of the blank strip, and what are the dimensions of the poster? 2 EXAMPLE: A poster has a rectangular printed area 100 cm by 140 cm, and a blank strip of uniform width around the four edges. The perimeter of the poster is 1 1 2 times the perimeter of the printed area. What is the width of the blank strip, and what are the dimensions of the poster? Solution: We are asked to find the width of the blank strip. So we let x = the width of the blank strip Then we translate the information in the Figure above into the language of algebra: Now we use the fact that the perimeter of the poster is 1 1 2 times the perimeter of the perimeter of poster = 3 2 perimeter of printed area 2(100 + 2 x ) + 2(140 + 2 x ) = 3 2 480 480 + 8 x = 720 8 x = 240 x = 30 The blank strip is 30 cm wide, so the dimensions of the poster are 100 + 30 + 30 = 160 cm wide by 140 + 30 + 30 = 200 cm long 3 EXAMPLE: A rectangular building lot is 8 ft longer than it is wide and has an area of 2900...
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Section_1.6-Modeling with Equations - Section 1.6 Modeling...

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