Math, asked by jyotisingha, 2 months ago

Find the value of the following:-​

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Answers

Answered by Yuseong
24

Answer:

2

Step-by-step explanation:

As per the provided information in the given question, we have been given that a:b = 1:2. We have been asked to calculate the value of,

  • \sf{\dfrac{4a+3b}{3a+b}}

As a:b = 1:2, let us suppose the value of a as x and b as 2x.

Now, we have the equation that is,

\longrightarrow\sf{\dfrac{4a+3b}{3a+b}}

Substitute the value of a and b that is x and 2x.

\longrightarrow\sf{\dfrac{4(x)+3(2x)}{3(x)+2x}}

Now, performing addition and multiplication then we'll peform addition in the order to find the required answer.

\longrightarrow\sf{\dfrac{4x+6x}{3x+2x}}

Performing addition to calculate the required answer.

\longrightarrow\sf{\cancel{\dfrac{10x}{5x}}}

Cancelling the terms,

\longrightarrow\boxed{\sf{\red{\dfrac{4a+3b}{3a+b} = 2}}}

Therefore, the required answer is 2.

\rule{200}2

Answered by Sɴɪɢᴅʜᴀ
27

Given :

  •  {\sf{What \:  is \:  the \:  value \:  of \:   \:   \dfrac{4a + 3b}{3a + b}  \:  \: if \:  a:b  \: = 1:2}}

Solution :

 \\  \sf \:  \: Let,  \:  \:  \:  \:  \tt a : b \: =  \:  \dfrac{a}{b}  \:  =  \:  \dfrac{1}{2}  = k \\   \\  \\  \tt \therefore a = k \:  \:  \: \:  \:  \:  \:  \:  \:   \:  \:  \:  \:  \:  \: b= 2k \\  \\

Now, we have the equation :

 \\  :  \implies \tt \dfrac{4a + 3b}{3a + b} \\  \\

Now, substituting the value of a and b in the equation :

 \\  \dashrightarrow   \:  \:  \:  \: \tt \dfrac{4a + 3b}{3a + b}  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \\  \\  \\  \tt \dashrightarrow  \:  \:  \:  \:  \tt \dfrac{4(k) + 3(2k)}{3(k)+ (2k)} \:  \:   \:  \\  \\  \\  \tt \dashrightarrow   \:  \:  \:  \: \tt \dfrac{4k + 6k}{3k+ 2k} \:  \:  \:  \:  \:  \:  \:  \:  \:  \: \\  \\  \\  \tt \dashrightarrow   \:  \:  \:   \tt \dfrac{10k}{5k} \:  \:  \:   \:  \:  \:  \:  \:  \:  \: \:  \:  \:  \:  \:  \:  \: \\  \\  \\  \tt  \ \dashrightarrow   \:  \: \tt \dfrac{ \cancel{10k}} { \cancel{{5}k}} \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \\  \\  \\   \dashrightarrow \: \:  \:  \pmb{ \mathfrak{2}} \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \\  \\

 \\  \:  \:  \:  \:  \:  \:  \:  \: { \boxed{ \mathfrak{ \pmb{Therefore, \:  \:  \:  \:  \:  \:  \dfrac{4a + 3b}{3a + b}  \:  \: =  \:  \:  \: 2}}}}  \:  \:  \: \bigstar \\  \\

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