When the digits of a two digit number are reversed, it is 9 less than 3 times the original number. The product of the digits is 14. What is the original number?
you can answer this in two ways~
systematic way (lol):
let x = units digit
let y = tens digit
from the second statement,
(1) xy = 14
from the first statement,
(2) 10x + y = 3(10y + x) - 9
from equation (1), we can express y in terms of x, yielding
y = 14/x
substituting this to equation (2),
10x + (14/x) = 3(10(14/x) + x) - 9
now you solve for x. then substitute this to y = 14/x to get y.
using trial and error:
i think this is easier since from the 2nd statement, the product of digits is 14 and 14 has few factors. the factors of 14 are
1, 2, 7, 14
here, we can't choose 1 and 14 since 14 cannot be in a single place digit (units.tens digit). thus we choose 2 and 7.
the possible numbers are 27 and 72. from the first statement, we check both. let's start with 27. when it is reversed, it becomes 72. is it 9 less than 3x the original?:
27*3 - 9 = 72
thus 27 is the number.
hope this helps~ :)