Question

So confusinggggggggggggggggg

Answer 1

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!

Answer 2

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`