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.
;
Let x = the numerator
then
(x+12) = the denominator
:
2/1 is just 2
:
{{{(x+16)/((x+12)-16)}}} = 2
which is
{{{(x+16)/(x-4)}}} = 2
:
x + 16 = 2(x-4)
:
x + 16 = 2x - 8
:
16 + 8 = 2x - x
:
24 = x
:
The original fraction = {{{24/36}}}
:
is this true?
{{{(24+16)/(36-16)}}} = 
{{{40/20}}} = 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)