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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 sat.collegeboard.org, 31% of the responses were correct.

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

Sequences

Link of the Day

Taking the SAT (or any test for that matter) can be very stressful. It can be difficult to relax and focus under pressure. In fact, often once you start panicking things only get worse. There are lots of different ways to manage test day stress. It's important to make sure that you get a good night sleep, eat a good breakfast (though you should avoid a really heavy breakfast), and arrive early at the testing site. You can find some great suggestions on how to minimize your test day stress here

6/11 Sequences

Always follow the Knowsys Method for math problems. It will save you time not only on the SAT, but also on math tests and quizzes in your school classes. Read the question carefully and identify the bottom line. Assess your options. Ask what you could do and then what you should do, and solve the problem quickly and efficiently once you have decided on a strategy. Finally, loop back to double check that you answered the question correctly.

8, a, 14, b, 20, ...

The first term of the sequence above is 8. Which of the following could be the formula for finding the nth term of this sequence for any positive integer n?


This problem really demonstrates how important it is to follow the Knowsys method (and to not skip steps). After reading the problem carefully and identifying the bottom line (you are looking for the formula for the nth term of this sequence), you may think that this requires the use of some complicated formula. If you are panicking right now because you can't remember what a geometric sequence is, or how to solve one, take a deep breath and relax. This problem is actually much simpler than that. Remember that step three of the Knowsys method is to assess your options. Ask yourself what could you do, and what should you do. You could try to solve this problem by writing a formula for the sequence, or you could simply work backwards and check the answers. You should solve this problem by working backwards because it is much easier and much faster.

(A) 2n + 6
(B) 3n + 5
(C) 5n + 3
(D) 6n + 2
(E) 6n + 5

We know that the first term in the sequence (when n = 1) must be 8, the third term in the sequence (when n = 3) must be 14, and the fifth term in the sequence (when n = 5) must be 20. Now all you have to do is try each formal and find the correct answer.

(A) works for the first term (since 2 * 1 + 6 = 8) but it fails for the third term (2 * 3 + 6 = 12, not 14).
(B) works for the first term (3 * 1 + 5 = 8), the third term (3 * 3 + 5 = 14), and the fifth term (3 * 5 + 5 = 20). Don't forget to loop back and verify that your answer matches the bottom line (it does). You now know this is the correct answer so you should simply bubble in (B) and move on from here.

For the sake of being thorough, here is an explanation of why the other answers do not work.

(C) works for the first term (5 * 1 + 3 = 8) but fails for the third term (5 * 3 + 3 = 18, not 14)
(D) works for the first term (6 * 1 + 2 = 8) but fails for the third term (6 * 3 + 2 = 20)
(E) fails for the first term (6 * 1 + 5 = 11)

The correct answer choice is (B).


On sat.collegeboard.org 46% of the responses were correct.

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