Question

Lin and Jen each thought of a number. Lin thought of a 2-digit number. Jen’s number is 7 times as big as Lin’s. But, if Lin writes 0 between the digits of her number, she’ll get Jen’s number. What are the numbers?

Answer 1

Let xy be the number of Lin. (x and y are the two digits)
Jen's number equals then 7(xy).
Add zero between the two digits of xy we get x0y.
And then we get x0y = 7(xy).
From the above equation we deduce y = 1
and also 7*x=x0 then x = 10

(please note, 10 is not a digit, but the equation has no solution otherwise )

Answer 2

Lin's number is 15 and Jen's number is 105.
15 is a two digit number and if we multiply it with 7, we get the answer 105.
15 x 7 = 105
And if we put 0 between the Lin's number that is 15, we will get 105
Thus, 15 and 105 are two numbers.