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Flashcards: Applying Percents to Word Problems

Portia purchased a laptop for $480, but after checking the merchant's website realized that she had been overcharged by 20%. By how much, in dollars, was she overcharged?

$48

$24

$96

$80

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Flashcards: Applying Percents to Word Problems

Portia purchased a laptop for $480, but after checking the merchant's website realized that she had been overcharged by 20%. By how much, in dollars, was she overcharged?

Your answer:

$48

Your answer:

$24

Your answer:

$96

Correct answer:

$80

Explanation:

In any percent problem, it is crucial that you know exactly which value the percent is to be taken of. Here Portia is overcharged by 20%, meaning that she paid 20% more than the item should have cost. That means that the amount she paid, $480, equals 20% more than she should have paid:

480=1.2(P) , where is the price she should have paid.

To solve for , divide both sides by 1.2 :

This means that she should have paid $400 but instead paid $480, so she overpaid by $80.

Note that a common mistake on percent problems is taking the percent of the wrong value: here you might be tempted to simply take 20% of 480, for example. The SAT test makers know that, and will often set up problems so that you're given the result of the percent change (here the result is Portia paying $480) and need to work your way back to the start value as you did here. Always pause to ensure that you know which value (or variable) gets multiplied by the percent change.

Flashcards: Applying Percents to Word Problems

Over the course of a single week, the price of a company’s stock rose by 10%. If the following week the company’s stock rose by 10% of the new price, by what percent did the stock increase over the two week period?

21%

120%

19%

20%

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Flashcards: Applying Percents to Word Problems

Your answer:

120%

Your answer:

19%

Your answer:

20%

Correct answer:

21%

Explanation:

This problem rewards students who do the work rather than just looking at a problem and going with what “looks right.” Whenever you see a problem that asks you to find the percent difference between two unknowns, you can probably pick your own numbers to make the problem easier since the problem is asking for a relationship rather than a value.

In this case, since you are dealing with percents, it is a good idea to start with the number 100. If you increase 100 by 10%, you will get

100+(0.1)(100)=110 after the first increase.

During the second week, you are told, the price of the stock increases by 10% of the new value. Be careful here to take the percent of the correct value, 110, rather than the original value. If you increase 110 by 10%, you get:

110+(0.1)(110)=121 .

To find the percent increase from there, you find the difference and then divide by the original before multiplying by 100:

\frac{11-100}{100}\times 100=21%

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Flashcards: Applying Percents to Word Problems

Flashcards: Applying Percents to Word Problems

Flashcards: Applying Percents to Word Problems

Flashcards: Applying Percents to Word Problems

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All SAT Mathematics Resources

Flashcards: Applying Percents to Word Problems

Flashcards: Applying Percents to Word Problems

Flashcards: Applying Percents to Word Problems

Flashcards: Applying Percents to Word Problems

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