SAT Math Study Tip # 4

Sat Math Study Tips

Is there any question type that the SAT test-writers love more than percents?  They must be smiling while they write them. A good study plan for the math section of the SAT ensures that you are ready for percent questions, as there will definitely be several of them on the test.

When you really think about it, there are two kinds of percent questions that are fairly straightforward.

For example, a “discount” question. If you get $3 off of the price of a $12 book, then $3 out of $12 is   $3/$12 ,  (3 divided by 12 on your calculator)  =  0.25 = 25%  off the price.

In the second example, if the population of a town of 4,000 people increases by 23% because a gold mine is discovered nearby, then 23% of 4,000 = 0.23 x 4,000 (on your calculator) = 1320 more people. Again, its fairly easy.

But there is one kind of % problem that is not straightforward at all. It’s the kind that tells you that “Sally saved $18 off the regular price of a pair of pants, which was a 30% discount off the regular price. What, then, is the regular price?” For this type of question we need a special method, called the proportion method, which is a method that allows us to think through a problem like this so that it makes sense to us, and that lets us calculate the answer quickly.

Here’s how it works:

First, we have to create a proportion that makes sense, and then do the calculation. That’s it.

Remember a proportion is two fractions that are equal to each other, that is, they are “in proportion”.

In the case of the discount problem with Sally above, we make our proportion by creating two fractions that make sense to us. We know that the “30% off” must be “in proportion” to the money that Sally saves compared to the regular price.

The proportion will be: 30/100  =   $18/?

But how did we decide what these fractions are?

Since 30%  = 30/100, the first fraction is easy.

The second fraction is not so easy, because we don’t know if the $16 should go on the top of the fraction or the bottom. But we can always decide this quickly, because of the way proportions work – if one fraction has a “smaller number over a bigger number”, then it has to be the same thing on both sides.

If Sally saved $18 off the regular price of the pants, then we know the regular price must be bigger than $18. So, the $18 goes on the top, and the unknown regular price goes on the bottom.

By replacing our question mark (?) with an “x” the proportion will now be:

To calculate a proportion, the rule is to multiple the top of one fraction by the bottom of the other fraction and to divide by the last remaining number. So, to calculate according to the rule of proportions:

x = (18) times (100) divided by 30  (on your calculator) =  $60

Therefore, the regular price is $60.

 

Let’s try another one:

Q:  The number of girls in Prairie Height high school increased by 65% one year, because a nearby school closed down. If there were 39 new girls in the school, then how many girls were there before the increase?

First: Let’s make our two fractions. Since the increase is 65%, the first fraction is easy, 65 /100

because the number of girls in the school last year “x” must have been bigger than 39.

Therefore  x =  (39) times (100) divided by 65 (on your calculator)  = 60 girls

Sat Math Tip:

Remember, percent problems like these ones can’t be solved in an easy way. The proportion method is powerful because it gives you a way to think of the two fractions separately, where it’s easier to make sense of them. When you put them together to make a proportion, then you have solved the problem, because the rule for calculating a proportion practically does the math for you! 

 


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