## SOLVING WORD PROBLEMS INVOLVING TWO NUMBERS

Solving Word Problems Involving Two Numbers :

In the section, we will learn how to solve word problems involving two numbers.

Example 1 :

The sum of the number and its positive square root is 7/36. Find the number.

Solution :

Let x be the required number

The sum of the number and its positive square root is 7/36.

x + √x  =  7/36

√x  =  (7/36) - x

By taking squares on both sides, we get

x  =  [(7/36) - x]2

x  =  (7/36)2 - 2 (7/36) x + x2

x  =  (49/1296) - (7x/18) + x2

1296x  =  49 - 504 x + 1296x2

1296x2 - 504x - 1296x + 49  =  0

1296x2 - 1800x + 49  =  0

(36x - 1) (36x - 49)  =  0

 36x - 1  =  0x  =  1/36 36x - 49  =  036x  =  49x  =  49/36

Therefore the required number is 1/36

Verification :

The sum of the number and its positive square root is 7/36.

(1/36) + √(1/36)  =  7/36

(1/36) + (1/6)  =  7/36

taking L.C.M we get

(1 + 6)/36  =  7/36

7/36  =  7/36

Example 2 :

The sum of two numbers is 15 and the sum of its reciprocals is 3/10. Find the numbers.

Solution :

Let x and y are the required two numbers

The sum of two numbers is 15

x + y  =  15

y  =  15 - x -----(1)

the sum of its reciprocals is 3/10

(1/x) + (1/y)  =  3/10

(y + x)/xy  =  3/10

10 (x + y)  =  3xy

10x + 10y  =  3xy  ---- (2)

Now we are going to apply the value of y in the second equation

10x + 10(15 - x)  =  3x(15 - x)

10x + 150 - 10x  =  45x - 3x2

3x2 - 45x + 150  =  0

By dividing the entire equation by 3, we get

x2 - 15x + 50  =  0

(x - 10) (x - 5)  =  0

 x - 10  =  0x  =  10 x - 5  =  0x  =  5

Therefore the two numbers are 10 and 5.

Verification :

The sum of two numbers is 15

10 + 5  =  15

15  =  15

the sum of its reciprocals is 3/10

(1/10) + (1/5)  =  3/10

Taking l.C.M we get,

(1 + 2)/10  =  3/10

3/10  =  3/10

After having gone through the stuff given above, we hope that the students would have understood how to solve word problems with two numbers.

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