Problem Solving Linear Functions

Models such as this one can be extremely useful for analyzing relationships and making predictions based on those relationships.

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With the help of equations in one variable, we have already practiced equations to solve some real life problems. Solution: Let one part of the number be x Then the other part of the number = x 10The ratio of the two numbers is 5 : 3Therefore, (x 10)/x = 5/3⇒ 3(x 10) = 5x ⇒ 3x 30 = 5x⇒ 30 = 5x - 3x⇒ 30 = 2x ⇒ x = 30/2 ⇒ x = 15Therefore, x 10 = 15 10 = 25Therefore, the number = 25 15 = 40 The two parts are 15 and 25. Then Robert’s father’s age = 4x After 5 years, Robert’s age = x 5Father’s age = 4x 5According to the question, 4x 5 = 3(x 5) ⇒ 4x 5 = 3x 15 ⇒ 4x - 3x = 15 - 5 ⇒ x = 10⇒ 4x = 4 × 10 = 40 Robert’s present age is 10 years and that of his father’s age = 40 years. You can figure out Two planes, which are 2400 miles apart, fly toward each other. At the end of one interest period, the interest earned was . The interest rate for the 00 investment is greater than the interest rate for the 00 investment. Let x be the interest rate for the 00 investment.Then the interest rate for the 00 investment is .Need help finding the From Ramanujan to calculus co-creator Gottfried Leibniz, many of the world's best and brightest mathematical minds have belonged to autodidacts.And, thanks to the Internet, it's easier than ever to follow in their footsteps (or just finish your homework or study for that next big test).When modeling scenarios with linear functions and solving problems involving quantities with a constant rate of change, we typically follow the same problem strategies that we would use for any type of function.Let’s briefly review them: Identify changing quantities, and then define descriptive variables to represent those quantities. Let x be the number of shirts Joe has and let y be the number of shirts Mark has.Your experience with travelling tells you how to figure this out: That is, Notice that you don't have to rely on just your memory to recall this formula. She runs full speed at 8 miles per hour for the race distance; then she walks back to her starting point at 2 miles per hour. Set the distances equal and solve for x: She spends 0.4 hours running and hours walking. One account pays interest, while the other pays interest. Since a total of 00 was invested, must have been invested at . After one interest period, the interest earned on a 00 investment exceeds the interest earned on a 00 investment by 0. According to the question; Ron will be twice as old as Aaron. Complement of x = 90 - x Given their difference = 12°Therefore, (90 - x) - x = 12°⇒ 90 - 2x = 12⇒ -2x = 12 - 90⇒ -2x = -78⇒ 2x/2 = 78/2⇒ x = 39Therefore, 90 - x = 90 - 39 = 51 Therefore, the two complementary angles are 39° and 51°9. If the table costs more than the chair, find the cost of the table and the chair. Solution: Let the number be x, then 3/5 ᵗʰ of the number = 3x/5Also, 1/2 of the number = x/2 According to the question, 3/5 ᵗʰ of the number is 4 more than 1/2 of the number. Solution: Let the breadth of the rectangle be x, Then the length of the rectangle = 2x Perimeter of the rectangle = 72Therefore, according to the question2(x 2x) = 72⇒ 2 × 3x = 72⇒ 6x = 72 ⇒ x = 72/6⇒ x = 12We know, length of the rectangle = 2x = 2 × 12 = 24Therefore, length of the rectangle is 24 m and breadth of the rectangle is 12 m. Then Aaron’s present age = x - 5After 4 years Ron’s age = x 4, Aaron’s age x - 5 4. Then the cost of the table = $ 40 x The cost of 3 chairs = 3 × x = 3x and the cost of 2 tables 2(40 x) Total cost of 2 tables and 3 chairs = 5Therefore, 2(40 x) 3x = 70580 2x 3x = 70580 5x = 7055x = 705 - 805x = 625/5x = 125 and 40 x = 40 125 = 165Therefore, the cost of each chair is 5 and that of each table is 5. If 3/5 ᵗʰ of a number is 4 more than 1/2 the number, then what is the number?