A word problem may be converted into an algebraic form according to the given condition of the problem with the help of signs and symbols.
From the condition of a particular given problem a student may construct a simple equation of one unknown or he is at liberty to construct the simultaneous equations of two or more unknowns for the same problem.
So construction of an algebraic equation from a word problem is very much important to solve the problem.
Example: -The sum of two digit number is 14. When 29 is subtracted from the number, the digits become equal. Find the number.
Solution: - Let the digits in the tens place and the unit place be x and y respectively.
So the number = 10 x + y
When 29 is subtracted from the number, it becomes
= (10 x + y) – 29
= (10 x + y) – (30 – 1)
= (10 x – 30) + y + 1
= 10 (x – 3) + (y + 1)
Therefore by the problem,
x– 3 = y + 1 … (1)
Or, x – y = 4 … (2)
And x + y = 14
Adding (1) and (2)
Similarly subtracting (1) from (2) then we will get y = 5
Therefore the number=10x+y=10(9) +5=95
Other example could be: -A does a work for 16 days and B does for 15 days. The wage of 4 days for A is less than the wages of 7 days for B by Rs. 4. If Rs. 500 is paid to them, find their daily wages.