Question

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

Answer 1

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.

Answer 2

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