Question

.Find the value of x in the proportion (x+5): (3x-6) = 3:8.

Answer 1

ANSWER:

Given:

• (x + 5) : (3x - 6) = 3 : 8

To Find:

• Value of x

Solution:

$\text{We are given that,}\\\\:\longrightarrow\sf(x+5):(3x-6)=3:8\\\\\text{So,}\\\\:\implies\sf\dfrac{x+5}{3x-6}=\dfrac{3}{8}\\\\\text{On cross-multiplying,}\\\\:\implies\sf8(x+5)=3(3x-6)\\\\\text{Solving the brackets,}\\\\:\implies\sf8x+40=9x-18\\\\\text{Transposing 8x to RHS,}\\\\:\implies\sf40=9x-8x-18\\\\\:\implies\sf40=x-18\\\\\text{Transposing 18 to LHS,}\\\\:\implies\sf40+18=x\\\\:\implies\sf58=x\\\\\bf{:\implies x=58}$

Verification:

$\text{We are given that,}\\\\:\longrightarrow\sf(x+5):(3x-6)=3:8\\\\\text{So,}\\\\:\implies\sf\dfrac{x+5}{3x-6}=\dfrac{3}{8}\\\\\text{Substituting value of x as 58,}\\\\:\implies\sf\dfrac{58+5}{3(58)-6}=\dfrac{3}{8}\\\\:\implies\sf\dfrac{63}{174-6}=\dfrac{3}{8} \\\\:\implies\sf\dfrac{63}{168}=\dfrac{3}{8}\\\\\text{Dividing numerator and denominator by 21 in LHS,}\\\\:\implies\sf\dfrac{3}{8}=\dfrac{3}{8}\\\\\text{LHS = RHS}\\\\\text{\bf{Hence Verified!!}}$