Solving Problems With Equations

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Here is a graphic preview for all of the Word Problems Worksheets.

You can select different variables to customize these Word Problems Worksheets for your needs.

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. Example 2 – Tom and Jerry have to stuff and mail 1000 envelopes for a new marketing campaign. If Tom helps, they can get the job done in 4 hours.

Walter can paint the house by himself in 12 hours and Helen can paint the house by herself in 16 hours.

How long would it take to paint the house if they worked 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.

How long would it take to fill the pool if both pipes were accidentally left open?

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.


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