Exercises: Percentages

In an e-sports tournament, $20\%$ of the $150$ participants play on a tablet, while the rest play on a computer. Calculate the exact number of players using a tablet to compete.

The loading bar of your favorite video game shows that $75\%$ of the total download has been completed. If the full file takes up $40$ GB, how many gigabytes have been downloaded so far?

Calculate the following percentages mentally using the division strategies learned in class (divide by $2$ for $50\%$, by $4$ for $25\%$ and by $10$ for $10\%$):

1. a) $50\%$ of $84$ viewers on a livestream.
2. b) $25\%$ of a $400$ gram pizza.
3. c) $10\%$ of a transit pass costing $700$ pesos.

Look at the following grid representing the plan of a leisure area in a shopping center. Each small square represents $1\%$ of the total. If the orange shaded area is reserved for arcade machines, what percentage of the total does this area occupy? Express the result also as an irreducible fraction.

A pair of sneakers that cost $1\,200$ pesos has a $15\%$ discount today. How many pesos do you save by buying them today? What is the final price you will pay for them?

Your cell phone indicates that it has $12\%$ battery left. If the total capacity of the battery is $4500$ mAh (milliampere-hours), how many mAh of power are left in the device exactly?

In a survey carried out in your 7th grade class, $18$ out of the $30$ students confirmed that they prefer horror movies to comedy movies. Calculate the percentage of students who prefer horror movies.

Hint: You can first write the ratio as a fraction $\frac{18}{30}$ and then find an equivalent fraction with a denominator of $100$.

Calculate, showing your reasoning at each step:

1. a) $200\%$ of $45$. (Think: $200\%$ of an amount is double its value.)
2. b) $150\%$ of $60$.
3. c) $0.5\%$ of $800$.
4. d) $300\%$ of $12$.

The battery of Lucía's tablet has a total capacity of $5000$ mAh. If after playing "Roblox" for a while she has $18\%$ battery left, how many mAh of power does she still have? What percentage of the battery has she already used?

In the vote to choose the activities for the school festival, $1200$ students took part. $65\%$ chose the sports tournament and the rest preferred the robotics workshop. How many students voted for the robotics workshop?

To organize the end-of-year trip, 7th grade students have sold raffle tickets. If they have already sold $360$ tickets, which represents $75\%$ of the total they had, how many tickets did they have in total to sell? How many do they still have left to sell?

An adventure video game takes up $12$ GB in a console's memory. If the system indicates that this game takes up $15\%$ of the total available memory, how many GB of capacity does the console's memory have in total?

In a multiple-choice mathematics exam with $40$ questions, a student answered $28$ questions correctly, got $8$ wrong and left $4$ blank. Calculate the percentage of correct answers, wrong answers and unanswered questions relative to the total. Check that the sum of the three percentages is $100\%$.

The price of a laptop in a store is $9\,000$ pesos excluding taxes. If $21\%$ VAT (Value Added Tax) must be applied, what will be the final price we will have to pay for the laptop?

Marta has posted a video on TikTok. In the first two hours, she has received $180$ likes. If she knows that $12\%$ of the people who watch the video like it, how many views has the video had in total during those two hours?

A neighbourhood had $1,200$ residents ten years ago and today has $3,000$.

1. a) By how many residents has the population increased?
2. b) What percentage increase does this represent compared to the number of residents ten years ago? Is it a percentage greater than or less than $100\%$? Interpret the result.

Percentages can also be smaller than $1\%$:

1. a) A saline solution contains $0.9\%$ salt. How many grams of salt are in a $500$ g bag of saline solution?
2. b) A batch of $2,000$ kg of flour contains $0.05\%$ impurities. How many kilograms of impurities does it contain?

In a trendy shoe store, a pair of sneakers costing $\$1\,700$ has a discount of $20\%$. However, as it is the last day of the sale, an additional discount of $10\%$ is applied to the already reduced price. What is the final price of the sneakers? Is it the same as applying a single discount of $30\%$? Justify your answer by calculating both cases.

Alex bought a computer to play his favorite video games. The final price he paid, including $21\%$ VAT, was $\$29\,040$. His friend tells him that the computer cost $\$24\,000$ before taxes. Is his friend right? Perform the necessary calculations to find the base price (excluding VAT) of the computer.

In a survey carried out at your school about social media use, $45\%$ of the students prefer Instagram, $35\%$ prefer TikTok and the remaining 48 students choose other platforms. How many students are there in total at the school? How many of them prefer Instagram?

A movie streaming service costs $\$9.99$ per month. If you decide to pay for the whole year at once, they offer a $15\%$ discount. However, this month there is a special promotion, and on top of that already reduced annual price, they offer a further fixed discount of $\$10$. How much will you save in total per year if you take advantage of both offers compared to paying month by month?

The storage of a cell phone is $128 \text{ GB}$. The operating system takes up $12.5\%$ of the total. If Álex has already used up $60\%$ of the remaining free space, how many gigabytes does he still have available to install new apps?

In a theater with a capacity of $750$ people, $12\%$ of the tickets were left unsold today. Of the tickets sold, $65\%$ were for adults and the rest for minors under 18 years old. How many minors under 18 attended the theater today?

A soft drink brand has decided to reduce the sugar content of its main drink. Previously, a $330 \text{ ml}$ can contained $35 \text{ g}$ of sugar. Now they have launched a version with a $40\%$ reduction in sugar and, in addition, they have increased the size of the can by $10\%$.

1. How many grams of sugar does the new can have?

2. What percentage of sugar does the weight of the sugar represent relative to the total volume in the new can? (Assume $1 \text{ ml} = 1 \text{ g}$ for the soft drink).

In the student council elections, candidate A obtained $30\%$ of the votes, candidate B obtained $25\%$, and candidate C received the remaining votes. If candidate C won with 27 votes more than candidate B, how many students voted in total? How many votes did each candidate receive?

The number of members in a youth book club has increased this year by $150\%$ compared to last year, when there were $24$ members.

1. a) A student says: "an increase of $150\%$ means that there are now $150$ members". Explain their mistake.
2. b) Calculate how many members there are now. Remember: an increase of $150\%$ means adding $150\%$ of the initial number to it.
3. c) If next year the club wants to triple last year's member count, what percentage increase does it need compared to last year?