you want to draw an enlargement of a design that is printed on a card that is 4in by 5in. you will be drawing this design on an piece of paper that is 8 1/2in by 11in. what are the dimensions of the largest complete enlargement you can make?

Question

anonymous · Answer

8x10 would be doubled the size and keep the same proportions anything larger would either be too large to fit on the new piece of paper or would distort the image. I believe that should be right at least.

anonymous · Answer

is there any way i can have a step by step of how this is solved

anonymous · Answer

Honestly I just used some common sense to think about it. 

You want to retain the proportions of 4x5. So you need to scale the picture by multiples of that so that the picture still remains those same proportions. So you need to find numbers that will multiply that could get you as close to 8x11.5 that you can get. You however need to multiply both by the same number so if you multiply by 2, double the size, you get. 8x10. If you do it by 2.5 you would get 10x11.5, which is too big. 2.25 would be 9x11.25....and on and on. So essentially what you are doing is finding

$$\frac{ 4 }{ 5}*\frac{ x }{ x}=\frac{ 8 }{ 11.5 } $$
This is turn can be written as 
$$\frac{ 4x }{ 5x}=\frac{ 8 }{ 11.5 }$$
Cross Multiply
$$45x = 40x => 45\neq40$$
Showing that no same x value will actually get you those proportions exactly. So at that point you need to just make an informed guess as to what the best choice you can do is.

anonymous · Answer

thanks