When you reverse the digits in a certain two-digit number you decrease its value by 18. what is the number if the sum of its digits is 12? a.92 b.75 c.45 d.86?

The number is 75

Lets start by defining the 2-digit number.


Define the number

Let x be the digit in the tens place and y be the digit in the ones place.
The number is 10x + y
The reverse of the number is 10y + x 

Now we will construct the equations needed


Construct equations

When the digits are reversed, the value decreases by 18:
(10x + y) - (10y + x) = 18 .    ← Apply distributive property
10x + y - 10y - x = 18            ←Combine like terms
9x - 9y = 18                           ←Divide by 9 through
x - y = 2

The sum of the digits is 12:
x + y = 12

Now that we have the two equations, we can solve for x and y.


Solve for x and y

x - y  = 2           (equation 1)
x + y = 12        (equation 2)


Make x the subject in equation 1

x - y = 2      ← Add y from both sides
    + y   +y       

x = 2 + y 


Substitute x = 2 + y into equation 2

x + y = 12                      ← Substitute x = 2 + y
2 + y + y = 12                ← combine like terms  
2 + 2y = 12                    ← Subtract 2 from both sides
-2           -2
2y = 10                          ← Divide by 2 on both sides
÷2    ÷2
y = 5


Substitute y = 5 into equation 1

x - y = 2                          ← substitute  y = 5
x - 5 = 2                          ← add 5 on both sides
   +5   +5
x = 7

Now we know the value of x and y. Lets find the 2-digit number.


Find the 2-digit number

The number = 10x + y = 10(7) + 5 = 75


The number is 75

Bis the right answer