Using Equations To Solve Word Problems

Using Equations To Solve Word Problems-70
Ratio Problems require you to relate quantities of different items in certain known ratios, or work out the ratios given certain quantities.This could be Two-Term Ratios or Three-Term Ratios Symbol Problems Variation Word Problems may consist of Direct Variation Problems, Inverse Variation Problems or Joint Variation Problems Work Problems involve different people doing work together at different rates.

Ratio Problems require you to relate quantities of different items in certain known ratios, or work out the ratios given certain quantities.This could be Two-Term Ratios or Three-Term Ratios Symbol Problems Variation Word Problems may consist of Direct Variation Problems, Inverse Variation Problems or Joint Variation Problems Work Problems involve different people doing work together at different rates.

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Consecutive Integer Problems deal with consecutive numbers.

The number sequences may be Even or Odd, or some other simple number sequences.

The equations are generally stated in words and it is for this reason we refer to these problems as word problems. If the two parts are in the ratio 5 : 3, find the number and the two parts.

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.

This may be for Two Persons, More Than Two Persons or Pipes Filling up a Tank For more Algebra Word Problems and Algebra techniques, go to our Have a look at the following videos for some introduction of how to solve algebra problems: Example: Angela sold eight more new cars this year than Carmen.

Using Equations To Solve Word Problems

If together they sold a total of 88 cars, how many cars did each of them sell? 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 involve Adding to a Solution, Removing from a Solution, Replacing a Solution,or Mixing Items of Different Values Motion Word Problems are word problems that uses the distance, rate and time formula.You may be asked to find the Value of a Particular Term or the Pattern of a Sequence Proportion Problems involve proportional and inversely proportional relationships of various quantities. Their difference = 48According to the question, 7x - 3x = 48 ⇒ 4x = 48 ⇒ x = 48/4 ⇒ x = 12Therefore, 7x = 7 × 12 = 84 3x = 3 × 12 = 36 Therefore, the two numbers are 84 and 36.3. If the perimeter is 72 metre, find the length and breadth of the rectangle.More solved examples with detailed explanation on the word problems on linear equations.6. After 5 years, father will be three times as old as Robert. Lever Problems deal with the lever principle described in word problems.Lever problem may involve 2 Objects or More than 2 Objects Mixture Problems involve items or quantities of different values that are mixed together.Then, we need to solve the equation(s) to find the solution(s) to the word problems.Translating words to equations How to recognize some common types of algebra word problems and how to solve them step by step: Age Problems usually compare the ages of people.

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