Question

Question # 40
If a/b = c/d = 4/5, then the simplified value of which of these expressions is equivalent to (4a-3c)/(5b+4d)?
Rei​

Answer 1

Given : a/b = c/d = 4/5

To Find :  simplified value of which of these expressions is equivalent to (4a-3c)/(5b+4d)

A. -8/65

B. 4/45

C. 8/45

D. 12/45

E. Cannot be determined.

Solution:

a/b = c/d  = 4/5  = k

a = bk

c = dk

(4a-3c)/(5b+4d)

= (4bk - 3dk) / (5b + 4d)

= k (4b - 3d)/(5b + 4d )

dividing numerator and denominator by d

= k (4b/d - 3 )/(5b/d + 4  )

Let say b/d  = m

= k ( 4m - 3)/ (5m + 4 )

k = 4/5

=  4 ( 4m - 3)/ 5(5m + 4 )

(4a-3c)/(5b+4d) = 4 ( 4m - 3)/ 5(5m + 4 )

a/b = c/d  = 4/5  = k

case 1 : Let say = a  = 4    , c = 4    then b = 5 ,  d = 5

b/d  = 1

Hence  (4a-3c)/(5b+4d) = 4 ( 4  - 3)/ 5(5  + 4 )  = 4 / 45

case 2  Let say = a  = 8    , c = 4    then b = 10 ,  d = 5

b/d  =2

Hence  (4a-3c)/(5b+4d) = 4 ( 4 (2) - 3)/ 5(5(2)  + 4 )  =  20 /70 = 2/7

Hence (4a-3c)/(5b+4d)  can not be determined

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Answer 2

${ \red{ \bf{ Given: }}}$

a/b = c/d = 4/5

${ \red{ \bf{ To \:Find: }}}$

simplified value of which of these expressions is equivalent to

${ \red{ \bf{ (4a-3c)/(5b+4d) }}}$

A. -8/65

B. 4/45

C. 8/45

D. 12/45

E. Cannot be determined.

${ \red{ \bf{ Solution:}}}$

a/b = c/d = 4/5 = k

a = bk

c = dk

(4a-3c)/(5b+4d)

= (4bk - 3dk) / (5b + 4d)

=k (4b-3d)/(5b + 4d )

dividing numerator and denominator by d

=k (4b/d-3)/(5b/d + 4 )

Let take, b/d = m

= k ( 4m - 3)/ (5m + 4)

k = 4/5

= 4( 4m - 3)/ 5(5m + 4)

(4a-3c)/(5b+4d) = 4( 4m-3)/ 5(5m + 4)

a/b = c/d = 4/5 = k

case 1: Let say = a = 4 5 , c = 4 then b = 5, d = b/d = 1

Hence (4a-3c)/(5b+4d) = 4(4-3)/ 5(5 + 4) = 4/45

case 2 Let say = a = 8 5 , c = 4 then b = 10, d = b/d =2

Hence (4a-3c)/(5b+4d) = 4( 4 (2) -3)/ 5(5(2) + 4) 20/702/7

${ \red{ \bf{ Hence\: (4a-3c)/(5b+4d) \:can \: not \:be \:determined }}}$