The sum of the digits of a certain two-digit number is 7. Reversing the digits decreases the number by 63. What is the number?

Answer 1

T+U = 7

U = 7-T

T=7-U

where U = the Unit's digit and T = the Ten's digit

UT = TU - 63

10U + T = 10T +U-63

replace U with 7-T

10(7-T) + T = 10T +7-T -63

expand, combine like terms

70-10T +T =10T -T -56

18T = 126

T=-126/18 = 42/6 = 7

U =7-T = 7-7=0

the oginal number is 70

try another way, trial and error, narrowing the possibilities down

Ten's digit is 7 minus the Unit digit

switch them and the number is 63 less than the original number

most original number could be is 90 something

try 92, which is 29 +63 = 92

but 9+2 = 11, not 7

try 80 something

81-18 = 63 but 1+8= 9, not 7

try 70, 70= 63+7

reverse 70 and you get 07

7+0 = 7

70-07= 63

the original 2 digit number is 70

which is the only solution

61 adds to 7, but can't be 63 more than 16

same with any 2 digit number in the 50's, 40's, 30s, 20's or 10's

only possible solutions would be in 70's 80s or 90s, 100's and you're into 3 digits

any integer in the 80s or 90s sums to more than 7

so a 70's number is the only solution. 72 through 79 sum to more than 7, so 70 is it, the only possible solution

Answer 2

Let "x" be the first digit in the initial number (the "tens" digit) and let "y" be the second digit in the initial number (the "ones" digit). That means the value of this number is "10x + y"

So the sum of the digits is 7 means:

x + y = 7

Reversing the digits means the number is now "yx" so to designate the value, we use: "10y + x". Since this decreases the value by 63 we can say:

10x + y = 10y + x + 63 or, by combing like terms we get:

9x - 9y = 63

If we divide both sides by 9 we get:

x - y = 7 or x = 7 + y

Plugging "7 + y" into our first equation (x + y = 7) in place of "x", we get:

7 + y + y = 7

2y = 0

y = 0

Plugging in y = 0 into out first equation (x + y = 7) we get:

x + 0 = 7

x = 7

So the number is 70

Answer 3

Let x be the 10's digit and y be the 1's digit. Let n be the number.

n=10x+y.

x+y = 7

The difference when reversing the digits.

10x+y -(10y+x) = 63

9x-9y = 63

Divide thru by 9

x-y = 7 --> x=7+y

Substitute for x.

(7+y) +y = 7

2y = 0

y=0

x=7+0 = 7

n = 10x+y = 70 +0 = 70