Question

Sa se afle valoarea raportului 5a+7b/2b+3a stiind ca a/b=3/8​

Answer 1

Răspuns:

Explicație pas cu pas:

a/b = 3/8 ⇒ a = 3  si b = 8

( 5a+7b)/(2b+3a) =

= (5×3 + 7×8)/(2×8+3×3) =

= (15+56)/(16+9)=

=71/25

______________________

Sau:  

a/b = 3/8 ⇒  8 a = 3 b ⇒ b = 8 a/3

( 5a+7b)/(2b+3a) = 71/25

= ( 5 a + 7× 8 a/3) / ( 2×8a/3 + 3a) =

= ( 15 a/3 + 56 a/3 ) : ( 16a/3 + 9a/3) =

= ( 71 a/3 ) : ( 25 a/3 ) =

= ( 71 a/3 ) × ( 3/25 a ) =

= 71/25

________________________

Sau:

a/b = 3/8 ⇒  8 a = 3 b

⇒  a/3 = b/8 = k → coeficient de proportionalitate

⇒  a = 3 k  si b = 8 k

( 5a+7b)/(2b+3a) = 71/25

= ( 5 × 3 k + 7 × 8 k ) / ( 2 × 8 k + 3 × 3 k ) =

= ( 15 k + 56 k ) / ) 16 k + 9 k ) =

= 71 k / 25 k =

= 71 / 25