Question

Find the value of the following:-​

Answer 1

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.

$\rule{200}2$

Answer 2

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 :

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

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