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
