![]() ![]() Robert’s father is 4 times as old as Robert. More solved examples with detailed explanation on the word problems on linear equations.Ħ. Solution: Let one part of the number be x Then the other part of the number = x + 10 The ratio of the two numbers is 5 : 3 Therefore, (x + 10)/x = 5/3 ⇒ 3(x + 10) = 5x ⇒ 3x + 30 = 5x ⇒ 30 = 5x - 3x ⇒ 30 = 2x ⇒ x = 30/2 ⇒ x = 15 Therefore, x + 10 = 15 + 10 = 25 Therefore, the number = 25 + 15 = 40 The two parts are 15 and 25. If the two parts are in the ratio 5 : 3, find the number and the two parts. A number is divided into two parts, such that one part is 10 more than the other. ![]() 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 = 6 Therefore, Aaron’s present age = x - 5 = 6 - 5 = 1 Therefore, present age of Ron = 6 years and present age of Aaron = 1 year.ĥ. According to the question Ron will be twice as old as Aaron. Then Aaron’s present age = x - 5 After 4 years Ron’s age = x + 4, Aaron’s age x - 5 + 4. Four years later, Ron will be twice as old as Aaron. Solution: Let the breadth of the rectangle be x, Then the length of the rectangle = 2x Perimeter of the rectangle = 72 Therefore, according to the question 2(x + 2x) = 72 ⇒ 2 × 3x = 72 ⇒ 6x = 72 ⇒ x = 72/6 ⇒ x = 12 We know, length of the rectangle = 2x = 2 × 12 = 24 Therefore, length of the rectangle is 24 m and breadth of the rectangle is 12 m.Ĥ. If the perimeter is 72 metre, find the length and breadth of the rectangle. The length of a rectangle is twice its breadth. Their difference = 48 According to the question, 7x - 3x = 48 ⇒ 4x = 48 ⇒ x = 48/4 ⇒ x = 12 Therefore, 7x = 7 × 12 = 84 3x = 3 × 12 = 36 Therefore, the two numbers are 84 and 36.ģ. What are the two numbers? Solution: Let the common ratio be x. Sum of two numbers = 25 According to question, x + x + 9 = 25 ⇒ 2x + 9 = 25 ⇒ 2x = 25 - 9 (transposing 9 to the R.H.S changes to -9) ⇒ 2x = 16 ⇒ 2x/2 = 16/2 (divide by 2 on both the sides) ⇒ x = 8 Therefore, x + 9 = 8 + 9 = 17 Therefore, the two numbers are 8 and 17.Ģ.The difference between the two numbers is 48. Solution: Then the other number = x + 9 Let the number be x. One of the numbers exceeds the other by 9. To practice solving two-step equations – word problems, feel free to use the worksheets below.Step-by-step application of linear equations to solve practical word problems:ġ. In this case – addition (subtraction) and multiplication (division). These word problems are called two-step because you have to perform two mathematical operations in order to solve them. If you multiply $4 that Janice paid per hour by the 5 hours she spend with that bike and then add the $10 she had to pay regardless of the time she spent with the bike, you will get a total sum of $30 that is indeed the full sum she paid. If you want to check the result – you can. Now that we have calculated the value of the variable, we can tell that Janice rented that bike for 5 hours. We will do that by dividing the whole equation by 4. The next thing to do is to get rid of the number 4 in front of the variable. To simplify things further, let us perform the subtraction. ![]() Now, in order to make things neater and more clear, let us move all the numbers (except for the number 4 – we have to get rid of it in a different way) to the right side of the equation. The cost of renting a bike is 10$ to take the bike and 4$ for every hour it spends in our possession. That means the number of hours is our variable. The thing we do not know is the number of hours Janice rented the bike for and we have been asked to find that out. For how many hours did she rent the bike?įirst thing we have to do in this assignment is to find the variable and see what its connection is with the other values. Hermione’s Bikes rents bikes for $10 plus $4per hour. But if you feel ready, we will show you how to solve it using this example: If you are not confident in your abilities to solve two-step equations with word problems, you can go to one-step equations – word problems and practice some more before continuing with this lesson. They are just a bit more complicated than one-step equations with word problems and they demand just a bit more effort to solve. Simply put, two-step equations – word problems are two step equations expressed using words instead of just numbers and mathematical symbols. ![]()
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