a two digit number is seven times the sum of its digits. The tens digit is three more than the units digit. What is the number.

Question

Iv\'ve been trying to do this for a long time and need Help. Make sure to include the steps. Thanks!

Answer 1

T is the 10s digit 

O is the one's digit <--- don't confuse the letter O with zero 0.

                                    My better judgement is telling me to use X instead of O;

                                     I'll bold it for you

 

The two digit number is 10T + O

 

It is 7 times the sum of the digits, so

 

 10T + O = 7(T+O)  <--- the 2 digit number is 7 times as large as the sum of the digits

 

 10T + O = 7T + 7O <--- distributive

 

 10T + O - 7T - 7O = 0 <--- everything to left side

 

 3T - 6O = 0 <--- combines like terms

 

 3(T - 2O) = 0 <--- factors out 3

 T - 2O = 0 <--- divides both sides by 3

 

 T = 2O = 2*O

 

BUT....

THe tens digit is 3 more than the one's digits, so

T = O + 3

 

Then we have  T = 2O = O  + 3

 

Subtracting O from both sides,

 O = 3

 

THe Tens digit is 6.

 

The number is 63.

The sum of the digits is 9.

9 x 7 = 63.

 

 

                        

Answer 2

o represents the one's digit

t represents the ten's digit

 

10t + o = 7(t + o)

10t + o = 7t + 7o

3t = 6o

t = 2o

 

t = o + 3       second condition

 

2o = o + 3

o = 3

 

What is the ten's digit? what is the numbr?