If you add the digits in a two-digit number and multiply the sum by 7, you get the original number. if you reverse the digits in the two-digit number, the new number is 18 more than the sum of its two digits. what is the original number?
a.250,250
b.315,185
c.370,230
d.410,90
e.480,20

The answer is A. 42

Solution:
Let x= ones digit, y=tens digit

1st condition (original number) : 7(x+y)=10y + x
2nd condition (new number by reversing the digits): 18+x+y=10x+y

simplifying:
1st condition: 6x=3y
2nd condition: x=2
substituting x=2 to 6x=3y
y=4

Let x be the first digit (ten's place) of the original number.
Let y be the second digit (one's place) of the original number.

(x + y)7 = original number
(x + y)7 = 10x + y
7x + 7y = 10x + y
6y = 3x

10y + x = (x + y) + 18
9y = 18
y = 2

6y = 3x
6(2) = 3x
12 = 3x
x = 4

x is the first digit, and y is the second digit, so the original number is 42.

(-14+3/2b) - (1+8/2b) = -5 -5/2b(-10+b) + (7b-5) = 8b-15(7/2b-3) - (8+6b) = -5/2b-11(5+2b) + (2b+3/2) = 4b+ 13/2