The ratio of [tex]a[/tex] to [tex]b[/tex] is [tex]6[/tex] to[tex]1[/tex] and the ratio of [tex]b[/tex] to [tex]c[/tex] is [tex]12[/tex] to [tex]1[/tex], then the value of [tex]\frac{2a + 3b}{4b + 3c}[/tex] is [tex]\frac{180}{51}.[/tex]
Ratio is used to compare to things i.e. numbers, size etc.
We have,
[tex]\frac{a}{b} = \frac{6}{1}[/tex] and [tex]\frac{b}{c} = \frac{12}{1}[/tex]
From the above given data we have to make value [tex]b[/tex] same in both ratios;
Therefore multiply [tex](\frac{a}{b})[/tex] ratios from [tex]12[/tex],
We get,
[tex]\frac{a}{b} = \frac{72}{12}[/tex] and [tex]\frac{b}{c} = \frac{12}{1}[/tex]
So,
[tex]a=72,\\b=12,\\c=1[/tex]
Now, putting above values in [tex]\frac{2a + 3b}{4b + 3c}[/tex],
[tex]=\frac{2(72) + 3(12)}{4(12)+ 3(1)}[/tex]
[tex]=\frac{180}{51}[/tex]
Hence we can say that The ratio of [tex]a[/tex] to [tex]b[/tex] is [tex]6[/tex] to [tex]1[/tex] and the ratio of [tex]b[/tex] to [tex]c[/tex] is [tex]12[/tex] to [tex]1[/tex], then the value of [tex]\frac{2a + 3b}{4b + 3c}[/tex] is [tex]\frac{180}{51}.[/tex]
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