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.Com
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) (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
:
= 2
which is
= 2
:
x + 16 = 2(x-4)
:
x + 16 = 2x - 8
:
16 + 8 = 2x - x
:
24 = x
:
The original fraction =
:
is this true?
=
= 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)
RELATED QUESTIONS
The denominator of the fraction is 2 more than the numerator. If 1 is subtracted
from... (answered by josgarithmetic,Edwin McCravy,ikleyn)
The denominator of a fraction is five more than the numerator. When 4 is subtracted from (answered by robertb)
Denominator of fraction is 6 more then the numerator. If one is added to numerator and 3... (answered by Boreal)
the numerator of a fraction is 8 less than the denominator. If 1 is added to the... (answered by ewatrrr)
The numerator of a certain fraction is 7 less than its denominator. If 4 is subtracted... (answered by edjones)
The denominator of a fraction is 6 more than the numerator . If one is added to numerator (answered by nerdybill)
If the denominator of a fraction is added to its numerator and the numerator is... (answered by checkley71)
If the denominator of a fraction is added to its numerator and the numerator is... (answered by stanbon)
If the denominator of a fraction is added to its numerator and the numerator is... (answered by checkley71)