Question

the sum of a 2 digit number and the 2 digit number when the digits are reversed is 77. if the difference of the same two numbers I'd 45, what are the two 2 digit numbers?​

Answer 1

61 an 16

Explanation:

a = original 10's digit

b = units

:

(10a+b) + (10b+a) = 77

11a + 11b = 77

simplify, divide by 11

a + b = 7

:

"the difference is 45."

(10a+b) - (10b+a) = 45

10a - a - 10b + b = 45

9a - 9b = 45

Simplify, divide by 9

a - b = 5

:

Use elimination here

a + b = 7

a - b = 5

-----------adding eliminates b, find a

2a = 12

a = 6

then

6 + b = 7

b = 7 - 6

b = 1

:

61 is the number

:

:

Check 61 + 16 = 77