If 9 is added to the original number, the new number will have the original digits reversed. Find the number. (Hint: let x = the tens digit and y = the ones digit, so that the value of the number is 10x + y).
Any help is greatly appreciated. Thanks.
2007-08-07 08:08:28 · 8 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
Let x = ten's digit of first number
y = unit's digit of first number
First number = 10x + y
Second number = 10y + x
Sum of digits x + y = 9
(10x + y) + 9 = (10y + x)
Solve into standard form:
9x - 9y = -9
9x + 9y = 81
18x = 72
x = 4
4 + y = 9
y = 5
So the first number is 45
The second number is 45+9=54, which is 45 with its digits reversed.
2007-08-07 08:18:28 · answer #1 · answered by Tony The Dad 3 · 2⤊ 0⤋
The sum of 2 digits of a certain number is 9
1) x + y = 9
If 9 is added to the original number, the new number will have the original digits reversed. Find the number
2) 10x + y + 9 = 10y + x
9x - 9y = - 9
x - y = - 1
x = y - 1
Substitute this into equation 1
x + y = 9
y - 1 + y = 9
2y = 10
y = 5
Plug this into equation 2
x = y - 1
x = 5 - 1
x = 4
Original number: 45
45 + 9 = 54
2007-08-07 15:19:58 · answer #2 · answered by kindricko 7 · 1⤊ 0⤋
BAsically this word problem means that 10x + y + 9 = 10y + x
Therefore 9x + 9 = 9y or x + 1 = y
Since you know that x + y = 9 you can just solve the equations (i will let you do a bit of work there) and you find that x = 4 and y = 5. Indeed 45 + 9 = 54.
2007-08-07 15:16:24 · answer #3 · answered by Christophe G 4 · 1⤊ 0⤋
Let the tens digit=x
& the ones digit=y
so x+y=9-----------------------(1)
&10x+y+9=x+10y------------(2)
from (2),we have
10x-x+y-10y+9=0
or 9x-9y=-9
or x-y=-1------------------------(3)
Adding (1) & (3),we have
2x=8
or x=4,putting this value in (1),we have
4+y=9
or y=9-4=5
so the no. is 4*10+5=45
now chk is 45+9=54 yes
2007-08-07 15:47:56 · answer #4 · answered by MAHAANIM07 4 · 1⤊ 0⤋
10x+y+9=10y+x
10x-x=10y-y-9
9x-9y+9=0 (/9)
x-y+1=0
x=y-1
Given: x+y=9.=> x=9-y=y-1
9+1=2y; 10=2y; y=5=> x= 5-1=4
Therefore, the original number is 45.
2007-08-07 15:22:00 · answer #5 · answered by IRENA 1 · 1⤊ 0⤋
All of the following qualify: 01, 12, 23, 34, 45, 56, 67, 78, 89.
2007-08-07 15:35:00 · answer #6 · answered by Tony 7 · 0⤊ 2⤋
x+y = 9
10x + y + 9 = 10y + x
9x - 9y = -9
x-y=-1
2x = 8
x=4
y=5
The original number is 45
2007-08-07 15:14:26 · answer #7 · answered by z_o_r_r_o 6 · 1⤊ 0⤋
x + y = 9
and 10x + y + 9 = 10y + x
You shoul dbe able to solbe it from here...
2007-08-07 15:18:17 · answer #8 · answered by tinfoil666 3 · 1⤊ 0⤋