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Worked-out word problems on linear equations with solutions explained step-by-step in different types of examples. Solution: Then the other number = x 9Let the number be x. Therefore, x 4 = 2(x - 5 4) ⇒ x 4 = 2(x - 1) ⇒ x 4 = 2x - 2⇒ x 4 = 2x - 2⇒ x - 2x = -2 - 4⇒ -x = -6⇒ x = 6Therefore, Aaron’s present age = x - 5 = 6 - 5 = 1Therefore, present age of Ron = 6 years and present age of Aaron = 1 year.5. Then the other multiple of 5 will be x 5 and their sum = 55Therefore, x x 5 = 55⇒ 2x 5 = 55⇒ 2x = 55 - 5⇒ 2x = 50⇒ x = 50/2 ⇒ x = 25 Therefore, the multiples of 5, i.e., x 5 = 25 5 = 30Therefore, the two consecutive multiples of 5 whose sum is 55 are 25 and 30. The difference in the measures of two complementary angles is 12°. ⇒ 3x/5 - x/2 = 4⇒ (6x - 5x)/10 = 4⇒ x/10 = 4⇒ x = 40The required number is 40.
In "real life", these problems can be incredibly complex.
This is one reason why linear algebra (the study of linear systems and related concepts) is its own branch of mathematics.
Step 1: A problem involving work can be solved using the formula , where T = time working together, A = the time for person A working alone, and B = the time for person B working alone.
In this case, one pipe is filling the pool and the other is emptying the pool so we get the equation: Step 2: Solve the equation created in the first step.
Example 1 – Walter and Helen are asked to paint a house.
Walter can paint the house by himself in 12 hours and Helen can paint the house by herself in 16 hours. 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?This can be done by first multiplying the entire problem by the common denominator and then solving the resulting equation. Click Here for Practice Problems Example 3 – One pipe can fill a swimming pool in 10 hours, while another pipe can empty the pool in 15 hours.How long would it take to fill the pool if both pipes were accidentally left open?Solving equations can be tough, especially if you've forgotten or have trouble understanding the tools at your disposal.One of those tools is the subtraction property of equality, and it lets you subtract the same number from both sides of an equation. Solving equations can be tough, especially if you've forgotten or have trouble understanding the tools at your disposal. This tutorial shows you how to take a word problem and translate it into a mathematical equation involving fractions.In this case, there are three people so the equation becomes: Step 2: Solve the equation created in the first step.This can be done by first multiplying the entire problem by the common denominator and then solving the resulting equation. One of those tools is the division property of equality, and it lets you divide both sides of an equation by the same number. Then, you'll see how to solve and check your answer. Many problems lend themselves to being solved with systems of linear equations.