Percentage - SAT Math

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Question

30% of what number is 20?

Solve to the nearest hundredth.

Answer

This is a very basic form percentage question. This can be rewritten:

0.3 * x = 20

(Remember, the word "of" in a word problem indicates multiplication, while the word "is" indicates an equals sign).

Solve for x: x = 20 / 0.3 = 66.67

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Question

The costs for Lizzie’s party are as follows: $6000 to cater, $1200 for the DJ, $2000 for decorating, and $2200 for the venue rental. Lizze can choose to apply a discount of 10% for the caterer and decorating but is then charged an additional 30% for the DJ and venue. What is the minimum price she will pay?

Answer

The discounts are not worth the extra cost. The answer is $11,400.

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Question

Mr. Glatfelter trains hunting dogs for a price of $4000 per dog. If it costs him $15,000 per month to keep his business open and each dog costs $1000 to train, how many dogs per month must he train to make a profit?

Answer

The answer is 6. 6 hunting dogs gives him a net profit of $3000. If you picked 5, that’s where Glatfelter breaks even (he doesn’t make a profit or a loss).

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Question

A dress was originally priced at $70. In January, it was put on sale for 20% off. Then in February, the sale price was lowered an additional $10 off of January's price. How much is the dress currently being sold for?

Answer

The dress started at $70. In January, it was marked down 20%. $70 * 0.2 = $14, so it was being sold for $70 – $14 = $56. Then we're told its price is again lowered, this time by $10. Now the price is $56 – $10 = $46.

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Question

The cost of manufacturing a single teddy bear is $6.25. A teddy bear company sells 200 bears for $1750. What is the profit percentage per single bear?

Answer

First we must find out what the price is for one teddy bear, manufactured by this company. Thus we divide 1750 by 200 and find that each bear costs $8.75. To find out the profit per bear, we divide 8.75 by 6.25 to arrive at 1.4. The bears are thus sold for 140% of what it costs to make them, giving a 40% profit.

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Question

When y is decreased by ten percent, the result is equal to fifteen percent of x. Assuming both x and y are nonzero, what is the ratio of x to y?

Answer

The problem states that decreasing y by ten percent gives us the same thing as taking fifteen percent of x. We need to find an expression for decreasing y by ten percent, and an expression for fifteen percent of x, and then set these two things equal.

If we were to decrease y by ten percent, we would be left with ninety percent of y (because the percentages must add to one hundred percent). We could write ninety percent of y as 0.90_y_ = (90/100)y = (9/10)y. Remember, when converting from a percent to a decimal, we need to move the decimal two places to the left.

Similarly, we can write 15% of x as 0.15_x_ = (15/100)x = (3/20)x.

Now, we set these two expressions equal to one another.

(9/10)y = (3/20)x

Multiply both sides by 20 to eliminate fractions.

18_y_ = 3_x_

The question asks us to find the ratio of x to y, which is equal to x/y. Thus, we must rearrange the equation above until we have x/y by itself on one side.

18_y_ = 3_x_

Divide both sides by 3.

6_y_ = x

Divide both sides by y.

6 = x/y

Thus, the ratio of x to y is 6.

The answer is 6.

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Question

Write 7.5% as a fraction.

Answer

First convert the percentage to a decimal:

7.5% = .075

Then turn this into a fraction:

.075 = 75/1000

Simplify by dividing the numerator and denominator by 25:

75/1000 = 3/40

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Question

Write as a fraction: 22%

Answer

22% = 22/100

Divide everything by 2:

22/100 = 11/50

11 is a prime number, so this is as reduced as this fraction can get.

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Question

25% of 64 is equal to 5% of what number?

Answer

25% of 64 is 16 (you can find this with a calculator by 0.25 * 64). Divide 16 by 0.05 (or 1/20) to get the value of the number 16 is 5% of. (Or mental math of 16 * 20)

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Question

Turn the following percentage into a fraction:

Answer

Since a percentage is a "part of 100" to turn it into a fraction we take the original number in the percent and place it over 100:

$65%\rightarrow \frac{65}{100}$

From here, simplify the fraction as necessary:

$\frac{65}{100}\div \frac{5}{5}=\frac{13}{20}$

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Question

Turn the following percentage into a fraction:

Answer

Since a percentage is a "part of 100" to turn it into a fraction we take the original number in the percent and place it over 100:

$22%\rightarrow \frac{22}{100}$

From here, simplify the fraction as necessary:

$\frac{22}{100}\div \frac{2}{2}=\frac{11}{50}$

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Question

Turn the following percentage into a fraction:

Answer

Since a percentage is a "part of 100" to turn it into a fraction we take the original number in the percent and place it over 100:

$46%\rightarrow \frac{46}{100}$

From here, simplify the fraction as necessary:

$\frac{46}{100}\div \frac{2}{2}=\frac{23}{50}$

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Question

Turn the following percentage into a fraction:

Answer

Since a percentage is a "part of 100" to turn it into a fraction we take the original number in the percent and place it over 100:

$55%\rightarrow \frac{55}{100}$

From here, simplify the fraction as necessary:

$\frac{55}{100}\div \frac{5}{5}=\frac{11}{20}$

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Question

Turn the following percentage into a fraction:

Answer

Since a percentage is a "part of 100" to turn it into a fraction we take the original number in the percent and place it over 100:

$72%\rightarrow \frac{72}{100}$

From here, simplify the fraction as necessary:

$\frac{72}{100}\div \frac{2}{2}=\frac{36}{50}\div \frac{2}{2}=\frac{18}{25}$

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Question

Turn the following percentage into a fraction:

Answer

Since a percentage is a "part of 100" to turn it into a fraction we take the original number in the percent and place it over 100:

$88%\rightarrow \frac{88}{100}$

From here, simplify the fraction as necessary:

$\frac{88}{100}\div \frac{4}{4}=\frac{22}{25}$

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Question

Turn the following percentage into a fraction:

Answer

Since a percentage is a "part of 100" to turn it into a fraction we take the original number in the percent and place it over 100:

$44%\rightarrow \frac{44}{100}$

From here, simplify the fraction as necessary:

$\frac{44}{100}\div \frac{4}{4}=\frac{11}{25}$

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Question

Turn the following percentage into a fraction:

Answer

Since a percentage is a "part of 100" to turn it into a fraction we take the original number in the percent and place it over 100:

$15%\rightarrow \frac{15}{100}$

From here, simplify the fraction as necessary:

$\frac{15}{100}\div \frac{5}{5}=\frac{3}{20}$

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Question

Turn the following percentage into a fraction:

Answer

Since a percentage is a "part of 100" to turn it into a fraction we take the original number in the percent and place it over 100:

$2%\rightarrow \frac{2}{100}$

From here, simplify the fraction as necessary:

$\frac{2}{100}\div \frac{2}{2}=\frac{1}{50}$

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Question

Turn the following percentage into a fraction:

Answer

Since a percentage is a "part of 100" to turn it into a fraction we take the original number in the percent and place it over 100:

$28%\rightarrow \frac{28}{100}$

From here, simplify the fraction as necessary:

$\frac{28}{100}\div \frac{4}{4}=\frac{7}{25}$

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Question

Turn the following percentage into a fraction:

Answer

Since a percentage is a "part of 100" to turn it into a fraction we take the original number in the percent and place it over 100:

$92%\rightarrow \frac{92}{100}$

From here, simplify the fraction as necessary:

$\frac{92}{100}\div \frac{2}{2}=\frac{46}{50}\div \frac{2}{2}=\frac{23}{25}$

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