Question

if a:b+c= 2:3 and b:a+c=3:7 Find a:b:c

Answer 1

This attachment is required answer.n

Answer 2

Given- a:b+c= 2:3 and b:a+c=3:7

Find- a:b:c

In mathematics, a ratio indicates how many times one number contains another. For example, if there are eight oranges and six lemons in a bowl of fruit, then the ratio of oranges to lemons is eight to six. Similarly, the ratio of lemons to oranges is 6:8 and the ratio of oranges to the total amount of fruit is 8:14

Proportion is explained majorly based on ratio and fractions. A fraction, represented in the form of a/b, while ratio a:b, then a proportion states that two ratios are equal. Here, a and b are any two integers.

Here,

$\frac{a}{b+c}=\frac{2}{3}$ ....(1) $\frac{b}{a+c}=\frac{3}{7}$ ....(2)

$\Rightarrow 3a=2b+2c$.....(3)

$\Rightarrow 7b=3a+3c$

$\Rightarrow 7b-3c$....(4)

Now, $2b+2c=7b-3c$ (combining 324)

$\Rightarrow 5b=5c \\\Rightarrow b:c=1:1$

$So, a=2+2=4$

$\Rightarrow a=\frac{4}{3}$

$a:b:c=\frac{4}{3}:1:1$

$=\frac{4}{3}\times 3:3:3=4:3:3$

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