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Writing Equations

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As you prepare for college, one of the best things that you can do for yourself, outside of studying, is to build good relationships with your teachers.  Learning the proper way to ask for help from your teachers can mean the difference between finally understanding a concept and getting written off as a whiner.  Read this article and think about how you can use the given advice not just in the future, but in your classes right now.

Algebra: Writing Equations

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

Always read each question carefully and make a note of the bottom line.  Assess your options for finding the bottom line and choose the most efficient method to attack the problem.  When you have an answer, loop back to verify that it matches the bottom line.

A florist buys roses at $0.50 a piece and sells them for $1.00 a piece. If there are no other expenses, how many roses must be sold in order to make a profit of $300?

Bottom Line: # roses = ?

Assess your Options:  You could find the profit from a single rose and then start plugging in answer choices, but that is not the fastest way to solve this problem.  A better way to solve this problem is to simply write an equation.  You could also solve this problem in a few seconds by using logic.

Attack the Problem:  Writing an equation will not take you much time.  Start by finding the profit from a single rose: $0.50.  (You know that the florist spends $0.50 to make each dollar, so $1.00 - $0.50 = $0.50.)

If each rose brings in a profit of $0.50, then how many must you sell to get $300?  Start by writing the fifty cents, and then use x to represent the unknown number of roses.  Each rose costs the same, so multiply the two numbers.  Together they must all equal $300.

$0.50x = $300.  (Just divide 300 by .5 to isolate the variable.)
         x = 600

Loop back: The x represented roses so you found your bottom line.  Look down at your answer choices.

(A) 100
(B) 150
(C) 200
(D) 300
(E) 600

The correct answer is (E).

Alternatively:  You can solve this problem in a few seconds.  Think about it logically; if you get less than $1 for each rose and you need $300, can you sell 300 roses and get the profit you need?  No!  You need more than $300 roses.  There is only one answer choice that works.


On sat.collegeboard.org, 71% of the responses were correct.

For more help with SAT math, visit www.myknowsys.com!