Question

Sum of three consecutive odd numbers is 309. Find the middle number.
Find the solution of the following equation:
[ (7x-1)/4 ] - 1/3 [ 2x - ((1-x))/2 ] = 19/3

Answer 1

AnswEr :

$\bf{\green{\large{\underline{\underline{\bf{Given\::}}}}}}$

Sum of three consecutive odd numbers is 309.

$\bf{\red{\large{\underline{\underline{\bf{To\:find\::}}}}}}$

The middle number.

$\bf{\purple{\large{\underline{\underline{\bf{Explanation\::}}}}}}$

$\bf{Let\;three\:consecutive\:odd\:numbers}\begin{cases}\sf{The\:1st\:number=x}\\ \sf{The\:2nd\:number=x+2}\\ \sf{The\:3rd\:number= x+4}\end{cases}}$

A/q

$\longmapsto\sf{x+x+2+x+4=309}\\\\\\\longmapsto\sf{3x+6=309}\\\\\\\longmapsto\sf{3x=309-6}\\\\\\\longmapsto\sf{3x=303}\\\\\\\longmapsto\sf{x=\cancel{\dfrac{303}{3} }}\\\\\\\longmapsto\sf{\red{x=101}}$

So,

• 1st number = x = 101.
• 2nd number = x+2 = 101+2 = 103.
• 3rd number = x+4 = 101+4 = 105.

∴ The middle number is 103.

____________________________________________

$\bf{\green{\large{\underline{\underline{\bf{Given\::}}}}}}$

$\sf{\large{\bf{\dfrac{(7X-1)}{4} -\dfrac{1}{3} \bigg[2x-1-\dfrac{x}{2} \bigg]=\dfrac{19}{3}} }}$

$\bf{\purple{\large{\underline{\underline{\bf{Explanation\::}}}}}}$

$\mapsto{\bf{\dfrac{(7x-1)}{4} -\dfrac{1}{3} \bigg[2x-1-\dfrac{x}{2} \bigg]=\dfrac{19}{3}}}\\\\\\\\\mapsto\bf{\dfrac{7x-1}{4} -\dfrac{1}{3} \bigg[\dfrac{4x-2-x}{2} \bigg]=\dfrac{19}{3}} \\\\\\\\\mapsto\bf{\dfrac{7x-1}{4} -\dfrac{4x-2-x}{6} =\dfrac{19}{3} }\\\\\\\\ \mapsto\bf{\dfrac{7x-1}{4} -\dfrac{3x-2}{6} =\dfrac{19}{3} }\\\\\\\\\mapsto\bf{\dfrac{21x-3-6x+4}{12} =\dfrac{19}{3} \:\:\:\ \underbrace{\sf{Taken\:L.C.M\:of\:4\:and\:6}}}\\\\\\\\\mapsto\bf{\dfrac{15x+1}{12} =\dfrac{19}{3} }}$

$\mapsto\bf{3(15x+1)=19\times 12\:\:\:\:\:\: \underbrace{\sf{Cross-multiplication}}}\\\\\\\\\mapsto\bf{45x+3=228}\\\\\\\\\mapsto\bf{45x=228-3}\\\\\\\\\mapsto\bf{45x=225}\\\\\\\\\mapsto\bf{x=\cancel{\dfrac{225}{45} }}\\\\\\\\\mapsto\bf{\red{x=5}}$

∴ The value of x is 5 .

Answer 2

Let the three consecutive odd no. be x,x+2 and x+4.

$\red{acc. \: to \: que.}$

Sum of three consecutive odd numbers is 309

$x + x + 2 + x + 4 = 309$

$3x + 6 = 309$

$3x = 303$

$x = \frac{303}{3}$

$\orange{x = 101}$

Now,

• x =101
• x+2=101+2=103
• x+4=101+4=105