the sum of the digits of a two-digit number is 13.If 27 is added to the number, the digits get interchange . What is the number
Answers
Answer:
ll say that the two digit number is AB where A is the tens digit and B is the ones digit (I'm not multiplying A and B).
AB can be rewritten as 10A + B.
The question tells me when I add the digits, I get 13.
A + B = 13
It also tells me that if I add 27 to the original number it reverses the digits:
AB + 27 = BA
Now by AB we actually mean 10A + B and by BA we actually mean 10B + A, so we rewrite this equation to be:
10A + B + 27 = 10B + A
Rewrite each side:
9A + (A + B) + 27 = 9B + (B + A) (one way to do this is to replace any A + B s I see with 13 because of the first equation I have)
9A + 27 = 9B
A + 3 = B (divide everything in the equation by 9)
Now I can substitute for B in that first equation:
A + B = 13
A + A + 3 = 13
A = 5
Then B has to add to this to give me 13, so B = 8.
My number is 58.
(Check: 5 and 8 add to 13, check. 58 + 27 = 85, check.)
Step-by-step explanation:
Answer:
58
Step-by-step explanation:
the two digit number is AB where A is the tens digit and B is the ones digit (I'm not multiplying A and B).
AB can be rewritten as 10A + B.
The question tells me when I add the digits, I get 13.
A + B = 13
It also tells me that if I add 27 to the original number it reverses the digits:
AB + 27 = BA
Now by AB we actually mean 10A + B and by BA we actually mean 10B + A, so we rewrite this equation to be:
10A + B + 27 = 10B + A
Rewrite each side:
9A + (A + B) + 27 = 9B + (B + A) (one way to do this is to replace any A + B s I see with 13 because of the first equation I have)
9A + 27 = 9B
A + 3 = B (divide everything in the equation by 9)
Now I can substitute for B in that first equation:
A + B = 13
A + A + 3 = 13
A = 5
Then B has to add to this to give me 13, so B = 8.
My number is 58.