The value of a two-digit number

Question

The value of a two-digit number is 10 more than 3 times the sum of its digits.  The units digit is 1 more than twice the tens digit.  What is the two-digit number?

Answer 1

Hi Shareeka,

 

Let x = the ten's digit

let y = the units digit

 

so

 

10x + y = 3(x+y) + 10  (this says the value of the two digit number is equal to 3 times the sum of the digits + 10

 

y = 2x +1      (the units digit is 1 more than twice the ten's digit

 

 

now substitute this new value for y back in the first equation

 

10x +(2x+1) = 3(x+2x+1) + 10

 

12x + 1 = 9x + 13

3x = 12

x = 4

 

y = 2x +1

y = 9

 

so our number is

 

49

 

49 = 3(4+9) +10

49 = 49

 

Hope this helps