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SAT Math: Algebra

Simultaneous Equations

Emmanuel owns a printing business.  He ordered boxes of copy paper for $10 each and boxes of photo paper for $12 each.  If Emmanuel ordered 10 boxes of paper and spent $112 (before tax), how many boxes of photo paper did he order?

A.  2
B.  3
C.  4
D.  6
E.  7

Knowsys Method

Read the problem carefully.  Be careful to identify the correct bottom line- which type of paper is the problem asking about?

Identify the bottom line.  boxes of photo paper = ?

Assess your options.  At Knowsys we call these problems “How Many? How Much?” problems.  To solve these problems, you can test out each of the answer choices, or you can create two simultaneous equations.  Unless the first answer choice you test out is correct, the latter strategy will save you time.  

Attack the problem.  Create two equations.   One should tell you “how many,” as in “how many boxes of paper are there total?”  The other equation should tell you “how much,” as in “how much do the boxes of paper cost?”  We will use c to represent copy paper and p to represent photo paper.

Screen Shot 2013-12-16 at 4.26.07 PM.jpg

The 10 and 12 in the second equation are the prices of each box.  The next step is to eliminate the variable that you are not focusing on, in this case, c.  To get rid of 10c in the second equation, you need to have -10c in the first equation, so multiply the entire first equation by -10 and then add the equations together to solve for p.  

Screen Shot 2013-12-16 at 4.26.16 PM.jpg

Loop back.  Did you solve for p (photo paper)? Yes.

The correct answer is D.

Want some help reviewing the math concepts you need to master?  Try out the Knowsys Pre-Algebra Flashcards, the Knowsys Algebra I Flashcards, and the Knowsys SAT & ACT Math Practice book.  

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