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So confusinggggggggggggggggg

So confusinggggggggggggggggg-example-1

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To Show:-

  • y = ( 7k - 2 )/( 1 - k)

Answer:-

The ratio given to us is ,


\implies (y + 2) : ( y + 7) = k : 1 \\

In fraction form we can write it as ,


\implies (y+2)/(y+7)=(k)/(1) \\

Now solve for y , by cross multiplying,


\implies 1( y + 2 ) = k( y + 7) \\

Simplify the brackets,


\implies y + 2 = ky + 7k \\

Subtract ky on both sides ,


\implies y - ky + 2 = 7k \\

Subtract 2 on both sides,


\implies y - ky = 7k - 2 \\

Take out y as common from LHS ,


\implies y ( 1 - k ) = 7k - 2 \\

Divide both the sides by (1-k) ,


\implies \underline{\underline{ \green{y =(7k-2)/(1-k)}}} \\

Hence Proved !

and we are done!

User Machineghost
by
8.1k points
2 votes

Convert the expression as follows:


  • \cfrac{y+2}{y+7} =\cfrac{k}{1} \ \ fraction\ form\ of\ the\ expression

  • y+2=k(y+7) \ cross-miultiply

  • y+2=ky+7k\ \ distribute

  • y-ky=7k-2\ \ collect\ terms\ with\ \ variable\ y

  • y(1-k)=7k-2\ \ factor\ out\ y

  • y=\cfrac{7k-2}{1-k}\ \ divide \ both\ sides\ by\ 1-k
User Yvan
by
7.8k points

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