A few days ago

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Can someone please help me with a math problem?

If the numerator of a certain fraction is increased by 6 and its denominator is decreased by 5, the resulting fraction is equal to 3/4. If the reciprocal of the original fraction is decreased by 1, the resulting fraction is 16/9. Find the original fraction.

thanks in advance!!

Top 1 Answers

A few days ago

Kia

Favorite Answer

Let x/y represent the original fraction

So this is what we have:

(x+6) / (y – 5) = 3/4

y/x – 1 = 16/9

Let’s simplify the first one

(x+6) / (y – 5) = 3/4

4(x+6) = 3(y – 5)

4x + 24 = 3y – 15

4x – 3y = – 15 – 24

4x – 3y = -39

Now let’s simplify the second one

y/x – 1 = 16/9

y/x = 16/9 + 1

y/x = 25/9

9y = 25x

25x – 9y = 0

Take the first equation and multiply both sides by -3

-3*(4x – 3y) = (-3)*-39

-12x + 9y = 117

Add this to the second equation

25x – 12x = 117

13x = 117

x = 117/13

x = 9

Now plug x into the second equation

25x – 9y = 0

25(9) – 9y = 0

225 = 9y

y = 225/9

y = 25

So the original fraction is 9/25

I hope this helped

Kia

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