the sum of digits of two-digit number is 15. interchanging the digits of this number increases it by 9. find the number

Question

translate this world problems to a system of equations

Answer 1

Let X = ones digit

Let T = tens digit

sum is 15 so, X +T = 15

X = 15 - T (eq. 1)

 

Interchanging digits:

original number = T x 10 + X

interchanged number = X x 10 + T

interchanged number = original number + 9

10X + T = 10T + X + 9

10T - T = 10X - X - 9

9T = 9X - 9 (eq. 2)

 

Substitute eq. 1 into eq. 2

9T = 9(15 - T) - 9

9T = 135 - 9T - 9

18T = 126

T = 7 

X = 8

 

Original number is 78

Interchanged number is 87

 

 

Answer 2

Hmmm.  I think the answer is 78 because the sum of 8 and 7 is fifteen and 87 is 9 more than 78.  But, you need two equations.  One equation could be: x + y = 15.

 

How about: 10x + y = 10y + x + 9

 

Solve: 9x = 9y + 9

            x = y + 1

 

Substitute x = 15 - y from first equation

 

15 - y = y + 1

 

Solve: y = 7, x = 8

Answer 3

Let x = units digit and y = tens digit

 

So, the number can be expressed as 10y + x

 

The number, if the digits are reversed, is 10x + y

 

We have:   x + y = 15

 

                10x+y = 10y+x+9

 

x + y = 15

9x - 9y = 9

 

x + y = 15

x - y = 1

 

2x = 16    x = 8 and y = 7

 

The number is 78.