The sum of the digits of a two-digit number is 7 and the difference between the number and that by reversing its digits is 9. Find the number.
2007-06-18 17:11:29 · 7 answers · asked by Prithika 2 in Science & Mathematics ➔ Mathematics
Let digits be a and b. Then the number is 10a + b
"sum of the digits is 7" => a+b=7 => b = 7-a
"difference between the number (10a + b) and that by reversing its digits (10b + a) is 9"
|(10a + b) - (10b + a)| = 9 (the difference could be + or -)
|9a - 9b| = 9
|a - b| = 1
Back-substitute b=7-a
|a - (7-a)| = 1
|2a - 7| = 1
=> 2a - 7 = +1 or -1
=> 2a = 8 or 6
=> a = 4 or 3
=> b = 3 or 4
=> The number was 43 (or 34)
2007-06-18 17:14:45 · answer #1 · answered by smci 7 · 0⤊ 0⤋
The number can be represented as AB. If the number were 12, A = 1 and B = 2.
Thus, A+B = 7, and AB - BA = 9.
Thinking about it, the answer is either 34 or 43. I can't tell by the way you worded the question.
2007-06-19 00:17:03 · answer #2 · answered by kashmir91086 2 · 0⤊ 0⤋
the numbers are 4 & 3. 43-34=9
2007-06-19 00:17:48 · answer #3 · answered by jonbel 3 · 0⤊ 0⤋
no is xy
x+y=7
y= 7-x
(10y+x)-(10x+y)=9
9y -9x =9
so y-x=1
substituting y= 7-x
7-x-x=1
7-2x=1
2x=6
x=3
so y = 4
so the number is 34 or 43
2007-06-19 00:16:33 · answer #4 · answered by sweet n simple 5 · 0⤊ 0⤋
a + b = 7
10a + b - (10b + a) = 9
10a + b - 10b - a = 9
9a - 9b = 9
a - b = 1
2a = 8
a = 4
b = 7 - 4 = 3
2007-06-19 00:23:27 · answer #5 · answered by Helmut 7 · 0⤊ 1⤋
34...43
2007-06-19 00:21:09 · answer #6 · answered by Bryan L 2 · 0⤊ 0⤋
x-y=9
x+y=7
2x=16
x=8
y=-1
shazzaaam
ok i didnt follow direction
2007-06-19 00:18:40 · answer #7 · answered by Anonymous · 0⤊ 0⤋