Question

If a/b = c/d = k and a,b,c,d are positive, then which of the following must be true?
A. (a+c)/(b+d)=k
B. ab=cd=k
C. ac=bd=k
D. a=c=k
E. ac/bd = k

Answer 1

if a/b = c/d
can i tell, a/c = b/d ?

Answer 2

what i did is multiply b on both sides and divide both sides by c

Answer 3

times b/c right?

Answer 4

yup

Answer 5

a/c = b/d
now add 1 on both sides, what u get ?

Answer 6

add 1??

Answer 7

yup,
add 1 to both sides and see what happens ?
a/c +1 = ... ?
b/d+1 = ...?

Answer 8

a+c / c
b+d / d

Answer 9

correct
so,
(a+c)/c = (b+d)/d
can you rearrange this ?

Answer 10

a+c / b+d = c/d = k
so A is correct

Answer 11

from that what does c/d equal ??

Answer 12

c/d=k

Answer 13

yup, you got it :)

Answer 14

so A must be true?

Answer 15

correct! :)

Answer 16

why B,C,D,E are not true then?

Answer 17

because ab, won't equal 'k'

ac = bd, but this won't equal k again,
ac = bd = kbd

a and c would not = k, unless b,d =1

lastly,
a/c =k, b/d = k, ac/bd = k*k = k^2 , not k

Answer 18

ok, i got it
thanks:)

Answer 19

welcome ^_^