pleas solve me this question.. math simultaneous equation?

Question

a number is formed by two digits whose sum is 9. it the digits are reversed the number is invreased by 45. find the number.

could you pleas tell me what "reversed" mean in maths?

Answer 1

if you have number written as xy, reversed is yx

x + y = 9
yx = 45 + xy

every number xy can be written as 10*x + y, so you can rewritte your equations as

x + y = 9
10*y + x = 45 + 10*x + y

x + y = 9
-9x + 9y = 45

x + y =9
-x + y = 5

y =7, x = 2

your number is 27

Answer 2

Consider :-
18, 27 ,36, 45 etc
reversed numbers are 81, 72, 54 etc

18 becomes 81 but 81 - 18 does not = 54
27 becomes 72 and 72 - 27 = 45 (bingo!)
Answer is 27

Answer 3

"Reversed" doesn't really occur only in math, because what is meant here is that for example, the reverse of digits of the number 31 is 13, the reverse of digits of the number 78 is 87, that for 56 is 65, and so on.

Other answers have given you the way to do it in simultaneous already, hope you could already see the meaning of "reversed" in this case.

Answer 4

let x be the tens digit

and y be the ones digit

(10x + y) is the original no.

x + y = 9

x = 9 -y ....eq. 1

(10y + x) is the new number when reversed

(10y + x) = (10x + y) + 45

10y + x = 10x + y + 45

9y = 9x + 45

y = x + 5 ...eq. 2

substitute eq. 1 to get:

y = 9 - y + 5

2y = 14

y = 7

x = 9 - y

x = 9 - 7

x = 2

(10x + y) = 10(2) + 7 = 27

so the answer is 27.

Answer 5

27 + 45 = 72

Answer 6

If we remedy the 1st equation for x in terms of y, we get x = 3 - 2y Now, if we plug that for the time of for x interior the 2nd equation, we get x^2 - 2y + 4y^2 = 18 (3 - 2y)^2 - 2y + 4y^2 = 18 9 - 12y + 4y^2 - 2y + 4y^2 = 18 9 - 14y + 8y^2 = 18 8y^2 - 14y - 9 = 0 Now, we are able to ingredient that into (4y - 9)(2y + a million) = 0 So, one in all 4y - 9 = 0 or 2y + a million = 0. meaning that 4y = 9 OR 2y = -a million y = 9/4 OR y = -a million/2 Now, if we plug those into our first equation, which we rearranged to x = 3 - 2y we get x = 3 - 2*(9/4) OR x = 3 - 2*(-a million/2) x = 3 - 9/2 OR x = 3 + 2 x = -3/2 OR x = 5 So, the solutions are (x, y) = (-3/2, 9/4) or (5, -a million/2). i wish that enables!

Answer 7

switch the digits, eg 12 becomes 21

x+y=9

10x+y-(10y+x)=45
10x+y-10y-x=45
9x-9y=45
x-y=5
x+y=9 add
2x=14
x=7
x+y=9
7=y=9
y=2
the original number is 27 & with digits switched it is 72