Question

show me the solution of these problem
if the numerator of a certain fraction is increase by 6 and its denominator is decrease by 5, the resulting fraction is equal to 3/4, if the reciprocal of the original fractionis decrease by 1, the resulting fraction is 16/9, find the origianl fraction?

Answer 1

x+6/y-5=3/4
(y-5/x+6)=16/9

I think this is how you set it up....

Answer 2

yea i think misterchyme did good. now you just have to solve the system of equations.

Answer 3

just show the first step

Answer 4

oh wait the second equation is (y-5/x+6)-1=16/9

Answer 5

show me please

Answer 6

well you would pick which equation looks the easiest to separate variables. I think the second one will actually be best for this..

First you would add one to each side and get
(y-5)/(x+6)=25/9

then multiply both sides by x+6
y-5=(x+6)25/9

solve for y in terms of x a then plug it into the other equation.. This one is going to get kinda messy, but should be fun! Can you take it from there?

Answer 7

im hanging, can u just show me how

Answer 8

am i going to find the lcd

Answer 9

hmm im going to have to think, the way i was going about it didnt really give a solution the x's just cancelled out

Answer 10

WOW I just posted the answer and the work... and it didnt show up.. /fail

Answer 11

x+6/y-5=3/4
(y-5/x+6)=25/9

OKAY lets try this again...
I am going to get rid of the fractions so it looks less intimidating and is easier to work with.. watch carefully
1st equation-
Take the reciprocal of 3/4 and multiply the other side by it

4(x+6)/3(y-5)=1
4x+24=3y-15
4x-3y=-39

2nd equation
Do the same thing but with 25/9( which is 1+16/9)

9(y-5)/25(x+6)=1
9y-45=25x+150
9y-25x=195

Now we have two equations that look much easier to work with

4x-3y=-39
-25x+9y=195

now what i would do is multiply your first equation by 3 and then your y's will cancel out and you can solve for x or you could do substitution.

Answer 12

Well I am about to go to bed so I will solve for x for you then you can do the rest..
Like I said multiply the first equation by 3 all the way through

12x-9y=-117
-25+9y=195
-13x=78
x=-6

Now that you have x=6 you can solve for y by plugging 6 in for x in either equation.