This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
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 Mary’s 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 Mary’s 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 Mary’s 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...
View
Full
Document
This note was uploaded on 01/23/2012 for the course MATH 8650 taught by Professor Kiryltsishchanka during the Spring '12 term at NYU.
 Spring '12
 KIRYLTSISHCHANKA
 Calculus, Algebra, Equations

Click to edit the document details