Math Word Problems - GED, PSAT, SAT, ACT, GRE Preparation 2.7 Word Problems - Numbers

Procedure:

Read the problem carefully and note down what is given and what is required.

Select a letter say x or y or z to represent the unknown quantity asked for.

Represent the word statements of the problems in the symbolic language step by step.

Look for quantities which are equal as per conditions given and form an equation.

Solve the equation.

Verify the result for making sure that your answer satisfies the requirements of the problems.

Example: Half of a certain number added to its one third makes it 40. What is the number. Solution:
Let the number be x.
Half of the number = x/2
One third of the number = x/3
As per condition of the problem
x/2 + x/3 = 40 ..........I
L.C.M. of the denominators 2 and 3 is 6.
Multiplying both sides of the equation by 6, we get
(3x+2x)/6 = 40
5x/6 = 40
5x = 40 * 6
5x = 240
x = 240/5
x = 48

Verification:
Substituting x = 48 in the equation I
L.H.S. = x/2 + x/3 = 48/2 + 48/3 = 24 + 16 = 40 = R.H.S.
Therefore x = 48 is the required number.

Directions: Solve the following word problems. Also write at least ten examples of your own.