SAT Math - How to find the part from the whole with percentage

An artist's new album sold copies on its release date. If the U.S. makes up of these sales, how many copies were sold on that day in the U.S.?

Explanation

Let's set up a proportion to solve this problem, where represents the number of copies sold in the U.S. Remember that we can express as a fraction.

$\frac{x}{900,000} = \frac{40}{100}$

Now, we can solve for the unknown by cross-multiplying.

is what percentage of

$8\frac{8}{9}%$

$\frac{9}{8}%$

Cannot be determined

Explanation

To solve this we need to set up a proportion.

$\frac{16}{180}=\frac{x}{100}$

Now we cross multiply

Divide by 180.

$x=\frac{1600}{180}=8\frac{8}{9}%$

A total of 200,000 votes were cast for two opposing candidates. If the losing candidate received 40% of the vote, how many votes did the winning candidate receive?

120,000

80,000

100,000

50,000

Explanation

60% of 200,000 is 120,000

0.6 * 200,000 = 120,000

What is 16% of 32?

Explanation

There are two ways to solve this problem.

First, we can convert the given percentage to a decimal and multiple by the whole.

16% = 0.16

Secondly, we could set up a proportion. We are given the whole from which a percentage is taken, so we can say:

$\frac{x}{32}=\frac{16}{100}$

To solve, cross multiply and simplify.

Your friend has 100 pounds of bacon and offers to share 45% of it with you. If you promised your mom 30% and your cousin 25% of your share, how many pounds of bacon do you end up with?

20.25 pounds

45 pounds

24.75 pounds

13.5 pounds

11.25 pounds

Explanation

Your share = 45% of 100 pounds of bacon = .45 * 100 = 45 pounds

For mom and cousin = 30% + 25% = 55%

Percent left for you = 100% - 55% = 45%

45% of 45 pounds = .45 * 45 = 20.25 pounds

Becky and Jason are running for class president, and each of the 30 students in the class voted. Becky received 60% of the votes. How many students voted for Jason?

Explanation

If Becky received 60% of the vote, Jason must have received 40% of the vote. 40% is equal to 0.40. By multiplying the number of votes times the percentage, we can calculate how many votes Jason received.

0.40 * 30 = 12.

The pie chart illustrates how Carla allocates her money each week.

If she spends $200 on groceries each week, how much does she spend on rent?

1000

500

350

450

750

Explanation

1. 20% of Carla's whole budget is equal to $200. With this information, one can find Carla's weekly budget.

Set up the equation: 0.2b = 200 (b = budget).

b = 200/0.2 = 1000 = Carla's weekly budget

2. To find the amount Carla spends for rent, one needs to find what 35% of $1000 is.

0.35 x 1000 = 350

3. Because Carla spends 35% of her total budget on rent, she spends $350 on rent.

Jane called one thousand times to tell you she's sorry. If you saw she was calling and let your phone go to voicemail of the time, how many voicemails would you have received if she left one each time?

None of the given answers

Explanation

To solve this problem, we can set up a proportion. Remember we can express percentages as fractions. Let represent the number of voicemails.

$\frac{x}{1,000} = \frac{67}{100}$

Now, we can cross-multiply and solve for the unknown.

Three salesmen, Gor, Levon, and Raffi, competed to sell the highest number of cars in the month of August. A total of 250 cars were sold.

Gor sold 100 cars. Levon sold 62% of the remaining cars, and Raffi sold the rest.

How many cars did Raffi sell?

Explanation

We first subtract the 100 cars that Gor sold from the total of 250 sold. We are left with 150 cars, and we know that Levon sold 62% of them. 100% – 62% = 38%. Hence, Raffi sold 38% of 150 cars. 150 * 0.38 = 57

There are pounds of cargo currently on a ship. After pounds have been taken from the ship and transferred to a warehouse, then, in terms of and , what percent of cargo is still on the ship?

$\dpi{100} \small \left [\frac{100\left (p-m \right )}{p} \right ]%$

$\dpi{100} \small \left [\frac{p}{100\left (p-m \right )} \right ]%$

$\dpi{100} \small \left [\frac{p-m}{100} \right ]%$

$\dpi{100} \small \left [\frac{100m}{p} \right ]%$

$\dpi{100} \small \left [\frac{100p}{m} \right ]%$

Explanation

If p is the number of pounds of cargo that is initially on the ship and m is the number of pounds of cargo that we transfer (or remove from the ship), we can find how many pounds of cargo are still on the ship after the transfer by the expression p – m. In order to model this as a percent, we would have to form a fraction, using the initial pounds of cargo, p, as the whole amount and p – m as the fractional part.

So,

we would get $\dpi{100} \small \frac{p-m}{p}$ as our fraction.

However, this problem asks us to find the percent, so we would simply multiply by 100

$\dpi{100} \small \left [\frac{100\left (p-m \right )}{p} \right ]%$ will get our answer into percent form.

How to find the part from the whole with percentage

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