Percentages: Worksheet with Answers

A school theater club sold 54 tickets for a performance. If the auditorium has 72 seats, what percent of the seats were sold?

54%
72%
75%
133%

What is 20% of 145?

A community garden has 240 plants. Of those plants, 35% are tomato plants. How many tomato plants are in the garden?

A bookstore received 240 notebooks in a shipment. Of those notebooks, 25% have spiral bindings. How many notebooks in the shipment have spiral bindings?

A gym charged a monthly membership fee of $48 during the summer and $60 during the winter. The summer membership fee was $p$% of the winter membership fee. What is the value of $p$?

A science museum recorded 54 student visitors during a special exhibit day. If 54 is $k$ percent of the total number of visitors that day, and there were 120 total visitors, what is the value of $k$?

A local food bank reported that 126 volunteers represented 70% of the total number of people who signed up to help during a community event. What was the total number of people who signed up?

A community center recorded the number of participants in several weekend workshops.

Workshop	Participants
Painting	84
Cooking	126
Robotics	63
Photography	147
Gardening	90
Total	510

The number of participants in the Photography workshop is $p$% of the number of participants in the Painting workshop. What is the value of $p$?

A manufacturing standard states that a batch of ceramic glaze may contain at most 0.004% cobalt by mass. If a batch has a total mass of 750 kilograms, what is the greatest allowable mass, in kilograms, of cobalt in the batch?

An online store buys a wireless speaker for $24. The store sets the selling price at 225% of the original cost. During a weekend sale, the speaker is offered at 60% off the selling price. What is the final sale price of the speaker, in dollars?

A factory produced 84 units of a device in January and 294 units of the same device in February. The February production was $k\%$ more than the January production. What is the value of $k$?

Quantity m is 175% of quantity n. Quantity m is also 48% of quantity p. What percent of quantity n is quantity p?

27%
274%
365%
840%

Answer key and explanations

1. Answer

75%

To find what percent 54 is of 72, divide the part by the whole and multiply by 100:

$\frac{54}{72}\times 100=0.75\times 100=75$

So, 75% of the seats were sold.

2. Answer

To find 20% of 145, convert 20% to a decimal: $20\%=0.20$. Then multiply: $0.20\times145=29$. Therefore, the correct answer is 29.

3. Answer

To find 35% of 240, convert 35% to a decimal: $35\%=0.35$. Then multiply:

$0.35\times 240=84$

So, there are 84 tomato plants in the garden.

4. Answer

Convert 25% to a decimal or fraction: $25\%=0.25=\frac{1}{4}$. Then multiply by the total number of notebooks: $0.25\times 240=60$. Therefore, 60 notebooks have spiral bindings.

5. Answer

To find what percent the summer fee is of the winter fee, divide the summer fee by the winter fee and multiply by 100.

$\frac{48}{60}=0.8$

$0.8 \times 100 = 80$

So, the summer membership fee was 80% of the winter membership fee.

6. Answer

Set up the percent equation using part = percent × whole:

$54=\frac{k}{100}(120)$

Divide both sides by 120:

$\frac{54}{120}=\frac{k}{100}$

$0.45=\frac{k}{100}$

Multiply by 100:

$k=45$

So, the value of $k$ is 45.

7. Answer

180

Let $x$ represent the total number of people who signed up. Since 126 is 70% of the total, write the equation:

$126 = 0.70x$

Divide both sides by $0.70$ to solve for $x$:

$x = \frac{126}{0.70} = 180$

So, the total number of people who signed up was $180$.

8. Answer

175

The Photography workshop has 147 participants, and the Painting workshop has 84 participants.

Set up the percent relationship:

$147=\frac{p}{100}(84)$

Divide both sides by 84:

$\frac{147}{84}=\frac{p}{100}$

$\frac{147}{84}=1.75$, so $\frac{p}{100}=1.75$.

Multiply by 100:

$p=175$

Therefore, the value of $p$ is 175.

9. Answer

0.03

Convert the percent to a decimal by dividing by 100:

$0.004\% = 0.00004$

Then multiply by the total mass:

$0.00004 \times 750 = 0.03$

So the greatest allowable mass of cobalt is $0.03$ kilograms.

10. Answer

21.6 / 108/5

The original cost is $24. A selling price that is 225% of the original cost is found by multiplying by $2.25$:

$24 \times 2.25 = 54$

So the selling price is $54.

A discount of 60% off means the customer pays 40% of the selling price:

$54 \times 0.40 = 21.6$

The final sale price is $\$21.60$, which is equivalent to $\frac{108}{5}$.

11. Answer

250

If February production was $k\%$ more than January production, then

$294=\left(1+\frac{k}{100}\right)(84)$.

Divide both sides by 84:

$\frac{294}{84}=1+\frac{k}{100}$.

Simplifying gives $3.5=1+\frac{k}{100}$.

Subtract 1 from both sides:

$2.5=\frac{k}{100}$.

Multiply by 100:

$k=250$.

12. Answer

365%

Translate each statement into an equation:

$m=1.75n$

$m=0.48p$

Since both expressions equal $m$, set them equal to each other:

$1.75n=0.48p$

Solve for the ratio $\frac{p}{n}$:

$p=\frac{1.75}{0.48}n\approx 3.6458n$

Convert the ratio to a percent:

$3.6458\times 100\approx 364.6$

So quantity p is approximately 365% of quantity n.