Example 1 :
Example 2 :
Example 3 :
Example 4 :
Example 5 :
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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