Algebra Equations: Translate

Link of the Day

A recent SAT Question of the Day involved the architect Frank Lloyd Wright.  On this date in history, one of Wright’s most famous buildings opened to the public.  The Guggenheim Museum opened its doors in 1959 and is now one of the wealthiest museums devoted to Modern art in the world.  If you are at all interested in art or architecture, consider using the Guggenheim opening as one of your excellent historical examples for the SAT essay.  You can find more information about the museum opening here and see photos from the event here.

10/21 Algebra

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

Use the same method for every math question on the SAT.  Read the question carefully, identify the bottom line, and assess your options for solving the problem.  Once you have identified an efficient method to solve the problem, attack it!  Before you choose an answer, loop back to verify that the answer addresses the bottom line.

If x + 2x is 5 more than y + 2y, then x – y =  

Bottom Line: x – y = ?

Assess your Options:  It would not be easy to work backwards and plug in answer choices for this problem.  Instead, translate the written words into a mathematical equation and solve for the bottom line.

Attack the problem:  Identify the terms in the original sentence that easily translate from English into math terms.  The word “is” translates to “equals,” and you know that if you need “more than” the original, you will be adding the specific number.  You can now write the information that you are given as a single equation: x + 2x = y + 2y + 5.  You can simplify this equation by combining like terms: 3x = 3y + 5.  With many other problems, you would want to solve the problem by isolating a variable.  However, you are only working with one equation, so you will need to solve for the bottom line and not a single variable.  Notice that your bottom line includes a positive x and a negative y on the same side of the equation.  You can rearrange your equation to create this: 3x – 3y = 5.  Now notice that the x and the y both have a three in front of the variable.  Factor out that three so that you have 3(x – y) = 5.  If you divide both sides by 3, you will find that x – y = .

Loop back:  You solved for your bottom line, so you are ready to look at the answer choices.

(A) -5

(B)

(C)

(D)

(E) 5

The correct answer is (D).

On sat.collegeboard.org, 44% of the responses were correct.

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