# Ratios

Freedom of the press has long been a hallmark of liberty in the United States.  However, many of the released SAT essay prompts have to do with balancing public and private lives, knowledge as a burden, and the abundance of information available through better technology.  Here is a current event that relates to all of these ideas:  a judge in the UK is calling for an independent group to regulate the press.  Think carefully about this current event, and decide where you stand on the issues that are raised.  If you decide to use this as one of your five current events, you will need to prepare a list of relevant details about this news story and a list of the broad topics that would let you know that this example relates to your essay prompt.

## Arithmetic: Ratios

Read the following SAT test question and then select the correct answer.

Use the same method for every math question on the SAT.  Start by reading the question carefully and identifying the bottom line.  Next, assess your options and choose the most efficient method to attack the problem.  When you have an answer, loop back to make sure that it matches the bottom line that you were asked to find.

Miguel is 180 centimeters tall. At 2:00 p.m. one day, his shadow is 60 centimeters long, and the shadow of a nearby fence post is t centimeters long. In terms of t, what is the height, in centimeters, of the fence post?
Bottom line: fence post = ?
Assess your Options:  Collegeboard.org uses a method that includes drawing the person and the post and then creating two right triangles.  That is a waste of time.  All you need to do is recognize that this is a ratio problem and set up your ratios correctly.
Attack the problem:  Set up the labels that you will use in your ratios so that you do not get confused about which number represents the length of the actual person and which number represents the length of his shadow.  You can set it up as actual divided by shadow:
$\frac{actual\: height}{shadow} = \frac{person}{his\: shadow} = \frac{post}{its\: shadow}$

Plug in the values that you know from the problem.  The only value that you do not know is the height of the post.  Leave that as a question mark so that you know which variable you must isolate.

$\frac{actual\: height}{shadow}= \frac{180}{60} = \frac{?}{t}$
All you need to do now is solve for the height of the post.  If you divide 180 by 60, the answer is 3.  You will need to multiply both sides by t to isolate the variable.  (Remember, you are solving for the question mark!)  Then you have your answer.

$3=\frac{?}{t}$

$3t = ?$
Loop Back:  The ? represented the height of the post in your original ratio, so you solved for your bottom line.  Look down at your answer choices.

(A) t + 120
(B) $\frac{t}{3}$

(C) 3t

(D) $3\sqrt{t}$
(E) $(\frac{t}{3})^{2}$