Digit problems

Question

The sum of the digits of a 2 digit number is 7, if the digits are reversed the new number increased by 3= 4 times the original number . Find the number

Answer 1

Let x = units digit and y = tens digit.  

 

Then the number can be expressed as 10y+x   (38 = 10(3) + 8, for example)

 

The number with digits reversed = 10x+y.

 

So, we have the system of equations:  x+y = 7

                                                         10x+y + 3 = 4(10y+x)

 

x+y = 7

6x - 39y = -3

 

Divide the second equation by 3 to obtain:    x+y =7

                                                                   2x - 13y = -1

 

Multiply the first equation by -2:  -2x - 2y = -14

                                                    2x - 13y = -1

 

Add the equations to get -15y = -15

 

                                   So, y = tens digit = 1

                                         x = ones digit =  7-y = 6

 

Thus, the number is 16.  

 

Therefore, the 

Answer 2

your choices are 16, 25, 34, 43, 52, 61, 70

16 becomes 61

61+3=64

64=4*16

16 is the answer