Writing Equations

Algebra: Writing Equations

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

Always read the question carefully and identify the bottom line.  Then assess your options and choose the most efficient method to attack the problem.  When you have an answer, loop back to make sure that your answer matches the bottom line; the specific question the problem asked you to solve.

The c cars in a car service use a total of g gallons of gasoline per week. If each of the cars uses the same amount of gasoline, then, at this rate, which of the following represents the number of gallons used by 5 of the cars in 2 weeks?

Bottom line: gal in 2 wks = ?

Assess your Options:  You could try to work backwards from the answer choices by plugging in a number for each variable, but you want to avoid working from the answer choices when you do not have to.  Instead, write an equation using the information that you are given in the problem.

Attack the Problem:  Start with the most basic information that you are given and logically translate the words into a math problem.  You know that c stands for cars and g stands for gallons of gasoline.  If all of the cars use the same amount of gasoline, then the total number of gallons must be divided evenly among each of the cars:

Now you know that there are 5 cars.  You might be tempted to put the 5 with the c, but think about it this way: that would mean that the same number of gallons was divided among more cars, so each car was using less gasoline, which is impossible!   If there are more cars, the total amount of gasoline must increase:

Now all you have to do is turn 1 week into 2 weeks by multiplying both sides of your equation by 2:

Loop Back: You found the gallons for 2 weeks, so look down at your answer choices.

(A) ten times c times g
(B) (2 times g) over (5 times c)
(C) (5 times g) over (2 times c)
(D) g over (10 times c)
(E)(10 times g) over c

The correct answer is (E).

Alternative method using Knowsys strategies:  If you struggle with writing equations, choose a number to represent the variable you are given in the problem.  You know you have 5 cars, but pick a number to represent the gallons that these cars use.  Any number that is not already in the problem will work; avoid  0 or 1 because multiple equations may work with these choices. Let’s say that g = 10.  In one week, those 5 cars will use 10 gallons.  How many gallons will they use in 2 weeks?  20 gallons!

Notice that the problem is a “which of the following” question.  Start with answer choice E instead of A.

Plug in the 10 for g and the 5 for c.  10 times 10 is 100, and then if you divide 100 by 5, you get 20.  That matches the answer that you found, so E must be correct.  None of the other answer choices will equal 20.  Strategies are tools to help you – remember that you get the same number of points for the correct answer no matter how you work the problem!

On, 31% of the responses were correct.

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