Question

Let 2a = 3b = 5c . (a)Find the ratio a : b : c . (b)If a - b + c = 55 , find c.

Answer 1

Answer:

$\boxed{\bf a:b:c=15:10:6} \\ \boxed{\bf c=30}$

Step-by-step explanation:

$\boxed{\bf Given,}\\\\ 2a=3b=5c\\\\ => 2a=3b\\ =>b=\frac{2a}{3}\\\\ =>2a=5c \\=>c=\frac{2a}{5}\\\\ \underline {(a) a:b:c=?}\\\\ \rightarrow a :b:c=a:\frac{2a}{3}:\frac{2a}{5}\\\\ \rightarrow a:b:c=1:\frac{2}{3}:\frac{2}{5}\\\\ \rightarrow a:b:c=\frac{15}{15}:\frac{2\times5}{3\times5}:\frac{2\times3}{5\times3}\\\\ \rightarrow \boxed{\bf a:b:c=15:10:6}\\\\ \underline{(b) \ a-b+c=55,c=?}\\\\ \rightarrow a-\frac{2a}{3} +\frac{2a}{5}=55\\\\ \rightarrow \frac{15a-10a+6a}{15}=55\\\\ \rightarrow 11a=55(15)$

$\rightarrow a=5(15) \\\\ \rightarrow a=75 \\\\ =>c=\frac{2a}{5} \\ \\ c=\frac{2(75)}{5} \\\\ c=2(15) \\\\\boxed{\bf c=30 }$

Answer 2

Answer:

c=30

Step-by-step explanation:

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