In this section, you will learn how to solve algebra word problems step by step.
Step 1 :
Read the question twice and understand the information clearly. Because, always it is very important to understand the information given in the question.
Step 2 :
If it is possible, we have to split the given information. Because, when we split the given information in to parts, we can understand them easily.
Step 3 :
Once we understand the given information clearly, solving the word problem in algebra will not be a challenging one.
Step 4 :
When we try to solve the word problems, we have to introduce "x" or y" or some other alphabet for unknown value ( = answer for our question). Finally we have to get value of the alphabet which was introduced for the unknown value.
Step 5 :
If it is required, we have to draw picture for the given information. Drawing picture for the given information will give us a clear understanding about the question.
Step 6 :
Using the alphabet introduced for unknown value, we have to translate the English statement (information) given in the question as mathematical equation.
In translation, we have to translate the following English words as the corresponding mathematical symbols.
of -----> x (multiplication)
am, is, are, was, were, will be, would be -----> = (equal)
Step 7 :
Once we have translated the English Statement (information) given in the question as mathematical equation correctly, 90% of the work will be over. The remaining 10% is just getting the answer. That is solving for the unknown.
These are the steps most commonly involved in solving word problems in Algebra.
Let us see how the above explained steps work in solving word problem in algebra.
Question :
The denominator of a fraction exceeds the numerator by 5. If 3 be added to both, the fraction becomes 3/4. Find the fraction.
Answer :
Step 1 :
In this problem, the denominator of the fraction is linked to the value in the numerator.
That is, the denominator of a fraction exceeds the numerator by 5
Once we get the value of the numerator, easily we can get the value of the denominator and find the required fraction.
Step 2 :
Let x be the numerator.
Then, the denominator of the fraction is (x + 5).
Therefore, the required fraction is
= x / (x + 5) -----(1)
Step 3 :
It is given that if 3 be added to both, the fraction becomes 3/4.
Then, we have
(x + 3) / (x + 5 + 3) = 3 / 4
Simplify and solve fore x.
(x + 3) / (x + 8) = 3/4
4(x + 3) = 3(x + 8)
4x + 12 = 3x + 24
x = 12
Step 4 :
Substitute 12 for x in (1)
(1)-----> x / (x + 5) = 12 / (12 + 5)
x / (x + 5) = 12 / 17
So, the required fraction is 12 / 17.
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