interpolation

\(\frac{4-2.4}{3.5-2.4}=\frac{311-240}{x-240}\)

 

First symplify the second equation

\(\frac{311-240}{x-240}= \frac{71}{x-240}\)

 

\(\frac{4-2.4}{3.5-2.4}=\frac{71}{x-240}\)

Apply the fraction cross multiply method

\((4-2.4)(x-240)=(3.5-2.4) * 71\)

 

Symplify the first equation

\((4-2.4)(x-240)\)\(= 1.6(x-240)\)

 

 

\(1.6(x-240) = (3.5-2.4)*71\)

 

Now symplify the second equation

\((3.5-2.4)*71 = 71 * 1.1 = 78.1\)

 

\(1.6(x-240) = 78.1\)

Multipy both sides by 10

\(10 * 1.6 (x-240) = 78.1 * 10\)

\(16(x-240) = 781\)

Then divide both sides by 16

\(\frac{16(x-240)}{16}=\frac{781}{16}\)

Symplify

\(x-240 = \frac{781}{16}\)

 

Now add 240 to both sides

\(x-240+240= \frac{781}{16}+240\)

\(x = \frac{4621}{16}\)

 

Hope this helps ;P