Statement Sums involving Linear Equations


 
 
Concept Explanation
 

Statement Sums involving Linear Equations

Statement Sums involving Linear Equation: In these sums a certain situation is given we have to analyse the statement and then suppose a certain quantity. and will then try to identify a relation with the quantity we have supposed.

The procedure to translate a word problem in the form of an equation is known as the formulation of the problem. Thus, the process of solving a word problem consists of two parts, namely, formulation and solution.

The following steps should be followed to solve a word problem:

Step I  Read the problem carefully and note what is given and what is required.

Step II Denote the unknown quantity by some letters, say x, y, z, etc.

Step III Translate the statements of the problem into mathematical statements.

Step IV Using the condition (s) given in the problem, form the equation

Step V Solve the equation for the unknown.

Step VI Check whether the solution satisfies the equation.

Example: The numerator of a fraction is 4 less than the denominatr. If 1 is added to both its numerator and denominator, it becomes 1/2. FInd the fraction.

Solution  Let the denominator of the fraction be x. Then,

Numerator of the fraction = x - 4

large therefore    Fraction large =frac{x-4}{x}

If 1 is added to both its numerator and denominator, the fraction becomes large frac{1}{2}.

large therefore    large frac{x-4+1}{x+1}=frac{1}{2}

large Rightarrow frac{x-3}{x+1}=frac{1}{2}

large Rightarrow 2(x-3)=x+1                           [ Using cross - multiplication]

large Rightarrow 2x-6=x+1

large Rightarrow 2x-x=6+1

large Rightarrow x=7

Putting x = 7 in (i), we get

Fraction large =frac{7-4}{7}=frac{3}{7}.  Hence, the given fraction is large frac{3}{7}.

 

Example : How much pure alcohol be added to 400 ml of a 15% solution to make its strength 32%?

Solution    Let x ml pure alcohol be added to 400 ml of a 15% solution to make its strength 32%. Here, 15% solution means that there is 15 ml pure alcohol in a solution of 100 ml.

Now, Quantity of alcohol in 100 ml solution = 15 ml

large therefore   Quantity of alcohol in one ml solution large =frac{15}{100};ml

       Quantity of alcohol in 400 ml solution large =frac{15}{100}times 400;ml=60; ml

       Total quantity of the solution = (400 + x) ml

       Total quantity of alcohol in (400 + x) ml solution = (60 + x) ml

large therefore    Quantity of alcohol in one ml large =frac{60+x}{400+x};ml

        Quantity of alcohol in 100 ml large large =frac{60+x}{400+x}times 100;ml

large Rightarrow   Strength of the solution large =left ( frac{60+x}{400+x} right )times   100%

But, the strength of the solution is given as 32%.

large therefore ;;frac{60+x}{400+x}times 100=32

large Rightarrow ;;100(60+x)=32(400+x)         [ Multiplying both sides by (400 + x)]

large Rightarrow ;;6000+100x=12800+32x

large Rightarrow ;;100x-32x=12800-6000

large Rightarrow ;;68x=6800

large Rightarrow ;;frac{68x}{68}=frac{6800}{68}

large Rightarrow ;;x=100

Thus, 100 ml alcohol must be added to make 32% strength of the solution.

Sample Questions
(More Questions for each concept available in Login)
Question : 1

Nitin subtracts thrice the number of pens he has from 60, he finds the resul to be 45. How many pens does he have?

Right Option : B
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Explanation
Question : 2

frac{3}{8} of number is less than the original number by 25. Find the number.

Right Option : D
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Explanation
Question : 3

A number is multiplied by 6 and 12 is added to the product. The result is 84. Then the number is ______________

Right Option : C
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Explanation
 
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