5lb Chapter 17 Question 9

[jaeun91]

Hi,

I'm having a hard time understanding the explanation for this question by M/P.

The question is: The "aspect ratio" of a computer monitor is the ratio of the monitor's width to its height. If a particular monitor has an aspect ratio of 16:9 and a perimeter of 100 inches, how many inches wide is the monitor?

The book explains the solution likes this: "Rather than assigning separate variables to the width and height, define them both in terms of the same unknown multiplier, based on the ratio given:

width: 16m
height: 16m"

My question is, why am i assigning the same variable to the width and height, when width and height are two different values?

Thank you.

[tommywallach]

Looks like you need to read up on ratios more (perhaps in our book on the subject). Remember, the 5lb. book is a book of sample questions, but it doesn't teach the methods/knowledge base from which this is built.

Ratios can always be expressed by means of an unknown multiplier that "holds" them in that ratio. Think of it this way: If you have a ratio of 2 to 3, the ACTUAL number of "thing" could be 2 things and 3 things, or 4 things and 6 things, or 6 things and 9 things. In the first example, the "unknown multiplier" is 1; in the second example, it's 2; in the third example, it's 3.

So you can set that multiplier to be a variable: x.

So if two things are in a ratio of 16 to 9, you can rewrite them as 16x and 9x.

Make sense?

-t

[tommywallach]

Side note: did you miswrite when you wrote 16m for BOTH of them? Did you mean "16m" and "9m"?

-t