Question

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

Answer 1

Answer:

I think 180

Step-by-step explanation:

(4(4)-3(4)) (5(5)+4(5))

(16-12) (25+20)

(4) (45)

180

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

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