A two digit number becomes 5/6th of itself when its digits are reversed. The two digits differ by 1. The number is
Answers
Answer:
54
Step-by-step explanation:
Because the given states that the two digits differ by one, we can set this problem up with one variable.
let x = the first digit and (x + 1) the second digit
A two digit number can then be 10x + (x + 1)
[the first digit times ten plus the second digit]
The reverse of that number would then be 10(x + 1) + x
[same reasoning as above but with x and (x + 1) reversed]
The first number becomes or is equal to 5/6 of the reversed number
Equation of this is 10x + (x + 1) = 5/6(10(x + 1) + x)
DISTRIBUTE
10x + (x + 1) = 5/6((10x + 10) + x)
SIMPLIFY
11x + 1 = 5/6(11x + 10)
MULTIPLY both sides by 6 [this leaves NO fractions]
6(11x + 1) = 6(5/6(11x + 10)
66x + 6 = 5(11x + 10)
DISTRIBUTE 66x + 6 = 55x + 50
SUBTRACT 55x and 6 from both sides
66x - 55x + 6 - 6 = 55x - 55x + 50 - 6
11x + 0 = 0 + 44
ADDITION IDENTITY [z + 0 = z]
11x = 44
DIVIDE both sides by 11
11x/11 = 44/11
1x = 4
MULTIPLY IDENTITY [1z = z]
x = 4 therefore x + 1 = 5
The first 2 digit number is 45 and the second is 54 (reverse the digits)
CHECK:
45 = 5/6(54)
MULTIPLY both sides by 6/5 [the reciprocal of 5/6[
6/5(45) = 6/5(5/6)54
54 = 1(54)
MULTIPLY IDENTITY [1z = z]
54 = 54 IT CHECKS