# HOW TO SOLVE WORD PROBLEMS IN ALGEBRA

Example 1 :

Example 2 :

Example 3 :

Example 4 :

Example 5 :

## Solving Word Problems in Algebra

Problem :

A number between 10 and 100 is five times the sum of its digits. If 9 be added to it, the digits are reversed. Find the number.

Solution :

Step 1 :

Let us understand the given information. There are two information given in the question.

1. A number between 10 and 100 is five times the sum of its digits.

2. If 9 be added to it, the digits are reversed.

Step 2 :

Target of the question :

What is that  number?

Step 3 :

A number between 10  and 100 is clearly a two digit number.

Introduce required variables for the information given in the question.

Let x be the digit  at one's place.

Let y be the digit at ten's place.

So, the number is xy and we have to find xy.

Step 4 :

Any two digit number can be written as given below.

56 = 10x5 + 1x6

(5 is at ten's place and 6 is at one's place)

In the same way we can write our two digit number xy.

That is,

xy = 10x + 1y

Now, translate the given information as mathematical equation using x and y.

Step 5 :

First information :

A number between 10 and 100 is five times the sum of its digits.

Translation :

A number between 10 and 100 :

xy = 10x + y

is ----> = (equal)

Five times sum of the digits :

5(x + y)

Equation related to the first information using x and y is

10x + y = 5(x + y)

10x + y = 5x + 5y

5x - 4y = 0 ----(1)

Step 6 :

Second Information :

If 9 be added to it, the digits are reversed.

Translation :

xy + 9 = yx

10x + 1y + 9 = 10y + 1x

9x + 9 = 9y

Divide both sides by 9.

x + 1 = y

or

y = x + 1 ----(2)

Step 7 :

Solve equations (1) & (2) :

Substitute (x + 1) for y in (1)

(1)----> 5x - 4(x + 1) = 0

5x - 4x - 4 = 0

x = 4

Substitute 4 for x in (2).

(2)----> y = 4  + 1

y = 5

Then,

xy = 45

Therefore, the required number between 10 and 100 is 45.

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