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Chen writes down a two digit number. He finds that if he swaps the digits of the numbers around, the new number he creates is three more than one third of the original number.
What is the original number?

Respuesta :

Answer:

The original number is 72

Step-by-step explanation:

72 swapping digits around results in 27

1/3 of 72 = 24

24 + 3 = 27

Answer:

Step-by-step explanation:

Let the two digit number be x in tenth place and y in unit place

Value of the digit = [tex]10x+y\\[/tex]

After swapping value of digit = [tex]10y+x\\[/tex]

Given that the new number he creates is three more than one third of the original number

one third of original number = [tex]\frac{10x+y}{3}[/tex]

3 more than the above = [tex]\frac{10x+y}{3}+3[/tex]

This equals new number

Hence [tex][tex]\frac{10x+y}{3}+3=10y+x\\10x+y+9 = 30y+3x\\7x-29y =-9[/tex][/tex]

Also x,y lie between 0 and 9.

Hence only possibility is x =7 and y =2

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