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Math word problems can be solved quite quickly if you know what you are looking for. Read the question a couple of times and note down any information that you are provided with. Always be clear about what value you are solving for; with bigger problems it's easy to lose track of this. It's good to get used to writing information down clearly as it helps you solve things faster. Learn with online tutors who will help you with word problems in math to get other tips and guidelines to solving them.

Solved Examples

Question 1: Find the numbers such that one-third of the first number added to twice of the second number gives 2 and four times of first number added to the five times the second number gives 5.
Solution:
Let the two numbers be x and y

Step 1:
Given,
One-third of the first number + twice of the second number = 2

=> $\frac{1}{3}$x + 2y = 2

=> x + 6y = 6                                   ...................................(1)

Also,
Four times of first number + five times the second number = 5

=> 4x + 5y = 5                               .......................................(2)

Step 2:

(1) => x = 6 - 6y, put in equation (2)

=> 4(6 - 6y) + 5y = 5

=> 24 - 24y + 5y = 5

=> - 19y = 5 - 24 = - 19

=> y = 1

Step 3:

Put y = 1 in x = 6 - 6y

=> x = 6 - 6 * 1 = 6 - 6 = 0

=> x = 0 

The solution to the system is x = 0 and y = 1.
 

Question 2: Amren starts his job with a certain monthly salary and earns a fixed increment every year. If his salary was 1500 dollars after 4 years of service and 1800 dollars after 10 years of service, what was his starting salary and what is the annual increment.

Solution:
Let Amren's staring salary = x dollar

Annual increment = y dollars


Step 1:

Salary in 4 years:

=> x + 4y = 1500                              .....................(1)

and salary in 10 years:

=> x + 10y = 1800                           .......................(2)

Step 2:

 Solve for x and y,

Subtracting equation (1) from equation (2)

=> x + 10y - ( x + 4y) = 1800 - 1500

=> x + 10y - x - 4y = 300

=> 6y = 300

=> y = $\frac{300}{6}$

=> y = 50

Put y = 50 in equation (1)

=> x + 4 * 50 = 1500   

=> x + 200 = 1500

=> x = 1500 - 200 = 1300

=> x = 1300

Answer: Starting salary of Amren = 1300 dollars and annual increment = 50 dollars.