The sum of the digits of a two-digit number is 9. The number with the digits reversed is 45 more than the original number. What is the original number?
i need to find the equation for it?
please help?
thankyou
2007-04-30 15:28:18 · 5 answers · asked by Clarity. 3 in Science & Mathematics ➔ Mathematics
i know the answer, i just don't know how to write the equation for it.
2007-04-30 15:34:23 · update #1
x + y = 9
(10y+x) - (10x+y) = 45
2007-04-30 15:34:54 · answer #1 · answered by mikedotcom 5 · 0⤊ 0⤋
Sum of two digit number is 9
5 + 4 = 9
5,4 in reverse is 45 + 9 = 54
the digits reversed is 45 more than the original number.
45 + 9 = 54 the original number
2007-05-01 20:19:06 · answer #2 · answered by mommy anie 3 · 0⤊ 0⤋
Ok...The number is XY.
so we know the first equation is
X+Y= 9
Now we need to find the next equation which is the inverse number. We can say XY = 10X+Y. suppose the number is 32. 10(3)+2 = 32.
x=3 y =2.
The equation should like this
10Y+X= 45+10X+Y
see how the inverse numbers of XY and YX are transformed following the rule above?
and the reversed are more than 45?
then you just simplify the equation
10Y+X= 45+10X+Y
10Y-Y+X-10X=45
-9X+9Y=45
that is our second equation we have the following syustem of equations
X+Y = 9
-9X+9Y= 45
lets use substitution solving for y with the above equation
Y= 9-X
-9X+9(9-X) =45
-9X+81-9X= 45
-18X= 45-81
-18X= -36
X= -36/-18
X= 2.
substitute in the second
Y= 9-X
Y= 9-2
Y=7
we refer to the number XY and plug the numebrs we found in the equations.
27
2007-04-30 16:03:21 · answer #3 · answered by Anonymous · 0⤊ 0⤋
a + b = 9
10a + b + 45 = 10b + a
9a - 9b = - 45
9a + 9b = 81
18a = 36
a = 2
b = 7
10a + b = 27
2007-04-30 15:41:22 · answer #4 · answered by Helmut 7 · 0⤊ 0⤋
It's 27.
2+7=9
72-27=45
I hope that helps!
2007-04-30 15:32:56 · answer #5 · answered by ohnoitstaytay 3 · 0⤊ 0⤋