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Question

The two digits in the numerator of a fraction whose value is 4/7 are reversed in its denominator. The reciprocal of the fraction is the value obtained when 16 is added to the original numerator and 5 is subtracted from the original denominator. Find the original fraction

Answer 1

ans 12/21

method
let x be 10's digit {numerator}
let y be units digit {numerator}
then numerator is 10x +y
and denominator is 10y+x
10x +y +16 = 10y+x-5
9x-9y=-21

Answer 2

Ok first is the first part, so a 2 digiit number in numerator which is reversed in the denomiter and is equal to 4/7. Well first you take 4/7 and times the numerator and denomitar by 3 so its 12/21. Then you find the reciprocal which is 21/12. Then since the original+16=21 The original Numerator is 5. then the Original Denomitor-5=12, so the original Denomitor is 17. So the Original Fraction is 5/17

Answer 3

Done as Algebra, 1st statement says

(10a+b)/(10b+a) = 4/7
40b + 4a = 70a + 7b
33b = 66a
b = 2a

2nd statement says

(10a + b + 16)/(10b + a - 5) = 7/4
40a + 4b + 64 = 70b + 7a - 35
33a - 66b = -99
2b - a = 3

substituting,

2(2a) - a = 3
4a - a = 3
3a = 3
a = 1
b = 2(1) = 2

fraction is 12/21

granted, 4/7 = 8/14 = 12/21 is simpler, but that's not the point of this kind of question.

Answer 4

Let u = the units digit and t = 10's digit of numerator.
Then (10t +u)/(10u+t) =4/7
40u+4t = 70t +7u
66t -33u =0
2t-u =0 <-- Eq1
(10t+u+16)/(10u+t -5) = 7/4
40t+4u+64= 70u +7t-35
33t -66u = -99
t-2u =-3 <-- Eq 2
-2t+4u =6 <-- Eq 3
Add Eq1 and Eq2 getting
3u = 6
u = 2
So t +4 = -3 --> t =1
So answer is 12/21

Answer 5

12/21 is the original fraction.

21/12 is the reciprocal fraction.

Answer 6

22

Now, if you want the real answer you need to do your own homework so that you understand the lesson being taught.

Answer 7

um i dont know

Answer 8

*retarded face* uhhhh i dont know *shurgs*