A few days ago
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
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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