SOLUTION: 1. The denominator of a fraction is 12 more than the numerator. If 16 is added to the numerator and 16 is subtracted from the denominator, the value of the resulting fraction is eq

Algebra ->  Expressions-with-variables -> SOLUTION: 1. The denominator of a fraction is 12 more than the numerator. If 16 is added to the numerator and 16 is subtracted from the denominator, the value of the resulting fraction is eq      Log On


   

Question 206147: 1. The denominator of a fraction is 12 more than the numerator. If 16 is added to the numerator and 16 is subtracted from the denominator, the value of the resulting fraction is equal to 2/1. Find the original fraction.
2. A number is 6 times the sum of its digits. The tens digit is 1 greater than the units digit. Find the number.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
1. The denominator of a fraction is 12 more than the numerator.
If 16 is added to the numerator and 16 is subtracted from the denominator,
the value of the resulting fraction is equal to 2/1.
Find the original fraction.
;
Let x = the numerator
then
(x+12) = the denominator
:
2/1 is just 2
:
%28x%2B16%29%2F%28%28x%2B12%29-16%29 = 2
which is
%28x%2B16%29%2F%28x-4%29 = 2
:
x + 16 = 2(x-4)
:
x + 16 = 2x - 8
:
16 + 8 = 2x - x
:
24 = x
:
The original fraction = 24%2F36
:
is this true?
%2824%2B16%29%2F%2836-16%29 =
40%2F20 = 2
:
:
2. A number is 6 times the sum of its digits.
The tens digit is 1 greater than the units digit.
Find the number.
:
Let x = the 10's digit; let y = the units
:
10x + y = "the two digit number"
;
10x + y = 6(x + y)
10x + y = 6x + 6y
10x - 6x = 6y - y
4x = 5y
:
The 10's digit is 1 greater than the units
x = y + 1
:
replace x with y+1
4(y+1) = 5y
4y + 4 = 5y
4 = 5y - 4y
y = 4
then
54 is the number
:
:
Is this true:
54 = 6(5+4)