-------------------------------------------------------------- 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
-------------------------------------------------------------- Answer: The number is 75 --------------------------------------------------------------
