SOLUTION: A TWO DIGIT NUMBER IS 7 TIMES THE SUM OF THE DIGITS. THE DIGITS GET INTERCHANGED IF 27 IS SUBTRACTED FROM THE NUMBER. FIND THE NUMBER

Question 477813: A TWO DIGIT NUMBER IS 7 TIMES THE SUM OF THE DIGITS. THE DIGITS GET INTERCHANGED IF 27 IS SUBTRACTED FROM THE NUMBER. FIND THE NUMBER
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
your 2 digits are x and y
10x + y = 7(x+y) is your first equation
10x + y - 27 = 10y + x is your second equation.
you need to solve these 2 equations simultaneously to get your answer.
before doing that, simplify each equation to get:
10x + y = 7(x+y) becomes:
10x + y = 7x + 7y
subtract 7x from both sides of the equation and subtract 7y from both sides of the equation to get:
3x - 6y = 0
hold on to that for now.
10x + y - 27 = 10y + x is your second equation.
add 27 to both sides of that equation and subtract 10y from both sides of the equation and subtract x from both sides of the equation to get:
9x - 9y = 27
hold on to that for now.
your 2 equations after being simplified are:
3x - 6y = 0
9x - 9y = 27
multiply both sides of the first equation by 3 to get:
9x - 18y = 0
9x - 9y = 27
subtract the first equation from the second equation to get:
9y = 27
divide both sides of this equation by 9 to get:
y = 3
substitute for y in the first equation of 3x - 6y = 0 to get:
3x - 18 = 0
add 18 to both sides of this equation to get:
3x = 18
divide both sides of this equation by 3 to get:
x = 6
your answers appear to be:
x = 6
y = 3
your first original equation says:
10x + y = 7(x+y)
substitute for x and y to get:
63 = 7(9)
this becomes 63 = 63 which is true, so the value for x and y plugged into the first original equation are good.
your second original equation says:
10x + y - 27 = 10y + x
substitute for x and y to get:
63 - 27 = 36
this becomes 36 = 36 which is true, so the value for x and y plugged ihto the second original equation are good.
your digits are 6 and 3.
the number is 63.

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