Question

If a:b=3:7 c:d=10:5 and 3a+2c:b+2d=5:3 find the ratio of a+b:c+d​

Answer 1

`(a+b)/(c+d) = (10)/(3)`

Explanation:

`(a)/(b) = (3)/(7)\\ \\ (c)/(d) = (10)/(5)\\ \\ (3a+2c)/(b+2d)=(5)/(3) \\\\a=(3)/(7)*b\\ \\c = (10)/(5)*d = 2d\\ \\(3((3)/(7)b +2d))/(b+2d) = (5)/(3) \\\\((9)/(7) b+6d)/(b+2d) =(5)/(3) \\\\(9)/(7) b + 6d = (5)/(3) (b+2d)\\\\(9)/(7)b+6d = (5)/(3)b+(10)/(3)d\\ \\ (9)/(7)b-(5)/(3)b+6d-(10)/(3)d=0\\\\-(8)/(21)b + (8)/(3) d= 0 \\\\`

`(8)/(3)d=(8)/(21) b\\ \\(21)/(8) *(8)/(3)d = b\\\\ 7d =b\\`

Find the ratio:

`a = (3)/(7)*(7d )\\a =3d\\\\\\b = 7d\\ d = (1)/(7)b\\\\c = 2d \\`

`c = 2((1)/(7) b )\\c = (2)/(7)b \\\\(a+b)/(c+d) = (3d+7d)/(2d + d)\\ \\ (10d)/(3d) = (10)/(3)`