Question
Find all two-digit numbers such that reversing the digits results in another two-digit number that is 75% larger than the original number.
Answers
Reiny
original:
let the unit digit be x
let the tens digit be y
number is 10y+x
number reversed = 10x+y
10x+y = 1.75(10y+x)
10x+y = 17.5y + 1.75x
8.25x = 16.5y
times 4
33x = 66y
x = 2y
# reversed#
12 21 ----> 21/12 = 1.75
24 42 ---> 42/24 = 1.75
36 63 etc.
48 84
So the number are 12, 24, 36, and 48
let the unit digit be x
let the tens digit be y
number is 10y+x
number reversed = 10x+y
10x+y = 1.75(10y+x)
10x+y = 17.5y + 1.75x
8.25x = 16.5y
times 4
33x = 66y
x = 2y
# reversed#
12 21 ----> 21/12 = 1.75
24 42 ---> 42/24 = 1.75
36 63 etc.
48 84
So the number are 12, 24, 36, and 48