Equation And Problem Solving

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.

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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.

Using a Formula is a problem-solving strategy that students can use to find answers to math problems involving geometry, percents, measurement, or algebra.

To solve these problems, students must choose the appropriate formula and substitute data in the correct places of a formula.

Justin can complete the project by himself in 6 hours, Jason can complete the project by himself in 9 hours, and Jacob can complete the project by himself in 8 hours.

How long would it take the triplets to complete the project if they work together?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. 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. 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?For example: Math problems requiring formulas can be simple, with few criteria needed to solve them, or they can be multidimensional, requiring charts or tables to organize students' thinking.Including more than one formula in a problem, or having multiple correct answers to a problem will help stretch this strategy.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 4 – One roofer can put a new roof on a house three times faster than another. How long would it take the faster roofer working alone?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 5 – Triplets, Justin, Jason, and Jacob are working on a school project.

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