The numerator of a fraction is 10 less than the denominator. If 4 is added to each, the value of the resulting fraction is 3/5. Find the original fraction.

I've tried using multiples of 3/5 and subtracting 4 from the numerator and denominator hoping it will give me a solution where the numerator is 10 less than the denominator but I want a faster way of figuring this problemo ut just in case I ever get it on a test.

I've tried using multiples of 3/5 and subtracting 4 from the numerator and denominator hoping it will give me a solution where the numerator is 10 less than the denominator but I want a faster way of figuring this problemo ut just in case I ever get it on a test.

This question still have no answer summary yet.

You could use this approach:
Let d = the denominator.
{{{((d-10)+4)/(d+4) = 3/5}}} Simplify then cross-multiply.
{{{(d-6)/(d+4) = 3/5}}}
{{{5(d-6) = 3(d+4)}}} Simplify and solve for d.
{{{5d-30 = 3d+12}}} Subtract 3d from both sides.
{{{2d-30 = 12}}} Add 30 to both sides.
{{{2d = 42}}} Divide both sides by 2.
d = 21
The original fraction is:
{{{(d-10)/d}}} or
{{{(21-10)/21}}}
{{{11/21}}} This is the original fraction.
Check:
Adding 4 to the numerator and to the denominator, we get:
{{{(11+4)/(21+4) = 15/25 = 3/5}}}

Did this answer your question? If not, ask a new question.

- If either 4 is added to the denominator of a fraction or 2 is subtracted from the numerator of the fraction, the resulting fraction is 1/2
If either 4 is added to the denominator of a fraction or 2 is subtracted from th...

- If the numerator of a certain fraction is increased by 5 and the denominator is decreased by 1, the resulting fraction is 8/3
If the numerator of a certain fraction is increased by 5 and the denominator is ...

- this is a math riddle that i can't do so please help i am a fraction eguivalent to 2/4 the sum of my numerator and my denominator is 21 what fraction am ihere it is help me please's
this is a math riddle that i can't do so please help i am a fraction eguivalent...

- The numerator of a fraction is one less than the denominator. If the numerator
The numerator of a fraction is one less than the denominator. If the numerator ...

- 12 1/3 + 7 7/15switch fractions to improper fractions then find a common denominator to find improper fraction of 12 1/3 multiply whole number (12) by the denominator of the fraction (3) then add the numerator of the fraction (1) t
12 1/3 + 7 7/15switch fractions to improper fractions then find a common denomin...

- If the numerator and denominator of a fraction are both decreased by one the fraction becomes 2/3
If the numerator and denominator of a fraction are both decreased by one the fra...

- When the numerator and the denominator of a fraction is the same - What is the fraction called
When the numerator and the denominator of a fraction is the same - What is the f...

- The numerator of a fraction is one more than the denominator
The numerator of a fraction is one more than the denominator...

- I could really use some help with this:
"The sum of the numerator and denominator of a fraction is 40
I could really use some help with this: "The sum of the numerator and denomina...

- The numerator of a fraction is 10 less than the denominator
The numerator of a fraction is 10 less than the denominator...