Answer:
20:35:91
Step-by-step explanation:
Given:
[tex]a:b=4:7\\ \\b:c=5:13[/tex]
Find:
[tex]a:b:c[/tex]
1. Since [tex]a:b=4:7,[/tex] then
[tex]a=4x\\ \\b=7x[/tex]
2. Since [tex]b:c=5:13,[/tex] then
[tex]b=5y\\ \\c=13y[/tex]
3. We have [tex]b=7x[/tex] and [tex]b=5y,[/tex] so
[tex]7x=5y\\ \\y=\dfrac{7}{5}x.[/tex]
4. Now,
[tex]a=4x\\ \\b=7x\\ \\c=13\cdot \dfrac{7}{5}x=\dfrac{91}{5}x,[/tex]
so
[tex]a:b:c=4x:7x:\dfrac{91}{5}x\\ \\a:b:c=20:35:91[/tex]
