Answer:
[tex]\frac{a+b}{c+d} = \frac{10}{3}[/tex]
Step-by-step explanation:
[tex]\frac{a}{b} = \frac{3}{7}\\ \\ \frac{c}{d} = \frac{10}{5}\\ \\ \frac{3a+2c}{b+2d}=\frac{5}{3} \\\\a=\frac{3}{7}*b\\ \\c = \frac{10}{5}*d = 2d\\ \\\frac{3(\frac{3}{7}b +2d)}{b+2d} = \frac{5}{3} \\\\\frac{\frac{9}{7} b+6d}{b+2d} =\frac{5}{3} \\\\\frac{9}{7} b + 6d = \frac{5}{3} (b+2d)\\\\\frac{9}{7}b+6d = \frac{5}{3}b+\frac{10}{3}d\\ \\ \frac{9}{7}b-\frac{5}{3}b+6d-\frac{10}{3}d=0\\\\-\frac{8}{21}b + \frac{8}{3} d= 0 \\\\[/tex]
[tex]\frac{8}{3}d=\frac{8}{21} b\\ \\\frac{21}{8} *\frac{8}{3}d = b\\\\ 7d =b\\[/tex]
Find the ratio:
[tex]a = \frac{3}{7}*(7d )\\a =3d\\\\\\b = 7d\\ d = \frac{1}{7}b\\\\c = 2d \\[/tex]
[tex]c = 2(\frac{1}{7} b )\\c = \frac{2}{7}b \\\\\frac{a+b}{c+d} = \frac{3d+7d}{2d + d}\\ \\ \frac{10d}{3d} = \frac{10}{3}[/tex]
