Question

If x:y= 3:4, find (3x+4y) : (5x+6y)

Answer 1

the answer is very simple.

=(3x+4y) : (5x+6y)
=(3×3 + 4×4) : (5×3+6×4)
=(9+16) : (15+24)
=25: 39
=25/39

Answer 2

Express y in term of x:

x : y = 3 : 4

⇒ x/y = 3/4

⇒ 3y = 4x

⇒ y = 4/3 x

Express: (3x + 4y) in term of y:

3x + 4y

= 3x + 4 (4/3 x)

= 3x + 16/3 x

= 25/3 x

Express (5x + 6y) in term of y:

5x + 6y

= 5x + 6(4/3 x)

= 5x + 24/3 x

= 13x

Express the ratio (3x+4y) : (5x+6y)

(3x+4y) : (5x+6y) = 25/3 x : 13 x

Divide by x :

(3x+4y) : (5x+6y) = 25/3 : 13

Multiply by 3:

(3x+4y) : (5x+6y) = 25 : 39

Answer: The ratio is 25 : 39