"Writing Systems of Equations" The sum of the digits of certain two-digit number is 9. Reversing its digits increase the number by 45. Find the number.
A) 36
B) 30
C) 27
D) 26

If the original number can be written as ab, where a is the digits in the tens place and b is in the ones place, then it can be expanded as

10a + b

where a and b are chosen from {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}. The sum of the digits is 9, so

a + b = 9

Reversing the digits gives the number ba, or

10b + a

which is larger than ab by 45, so

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

-9a + 9b = 45

a - b = -5

Solve for a and b :

(a + b) + (a - b) = 9 + (-5)

2a = 4

a = 2

Then

a + b = 9

2 + b = 9

b = 7

So the original number if (C) 27.

your answer is -9

step-by-step explanation: