Exercises: Proportional sharing

Three siblings decide to share a bag of $120$ candies directly proportionally to their ages, which are $2$, $3$ and $7$ years old. How many candies does each one receive?

Three friends, Ava, Ben and Cal, have collaborated in a charity market selling crafts. They decide to share the $300 \ \$$ profit directly proportionally to the number of hours each one has worked: Ava worked $2$ hours, Ben $3$ hours and Cal $5$ hours. Calculate how much money each one receives.

In a video game competition, $100$ bonus points are shared between two players inversely proportionally to the number of mistakes they have made. If the first player has made $2$ mistakes and the second has made $4$ mistakes, how many points does each one receive?

A photographer has taken a total of $180$ photos during a trip. She wants to organize her album by sharing the photos directly proportionally to the days she spent in each city: $4$ days in Chicago, $5$ days in Dallas and $9$ days in Boston. How many photos will she put in each city's section?

A carpenter has a wooden board of $240 \text{ cm}$ and needs to cut it into three pieces whose lengths are proportional to the numbers $1$, $2$ and $3$. What will be the length of each piece?

A prize of $770 \ \$$ is to be shared among the top three finishers of a school race inversely proportionally to the position obtained (1st, 2nd and 3rd place). What amount of money does each of the three winners receive?

A group of three YouTubers has received a reward of $450 \ \$$ for a joint video. They have decided to share the money directly proportionally to the number of videos each one has uploaded to the channel that month: $4$, $5$ and $6$ videos respectively. How much money will each one receive?

Two students, Julia and Marcus, have to share $10$ hours of gaming console time during the weekend. As Julia has got better grades, they decide to share the time inversely proportionally to the number of failed subjects: Julia has failed $4$ subjects and Marcus has failed $6$. How many hours of gaming does each one receive?

Three friends decide to rent a private server to play an online video game during the holidays. The total cost of the rent is $153\ \$$. They have agreed to share the payment directly proportionally to the time each one has been connected: Alex was connected for $12$ hours, Bea for $18$ hours and Christian for $21$ hours. How much must each one contribute to pay the bill?

An environmental association has received a grant of $2\ 160\ \$$ to reward three volunteers who have participated in cleaning the beaches. The money will be shared directly proportionally to the number of bags of waste collected by each one. If the first volunteer collected $24$ bags, the second $30$ bags and the third $36$ bags, calculate the financial amount that each volunteer receives.

In a drone race, $310$ bonus points are shared among the top three finishers inversely proportionally to the number of technical faults they have committed during the circuit. The first finisher had $2$ faults, the second had $5$ faults and the third had $10$ faults. How many points does each one receive?

Three siblings help with the household chores and their grandfather decides to give them a reward of $114\ \$$ for their savings. However, to encourage responsibility, he shares the money inversely proportionally to the number of times they have forgotten to tidy their room this month. Lucy forgot $2$ times, George $3$ times and Emma $6$ times. What amount of money will each one receive?

A small graphic design studio has made a profit of $5\ 400\ \$$ from an advertising project. The director decides to share the profit among his three employees directly proportionally to the years of experience they have in the company. Employee A has been there for $2$ years, employee B for $4$ years and employee C for $6$ years. Calculate the share of the profit that each worker receives.

In an archery competition, $135$ handmade arrows are shared among the three best archers inversely proportionally to the distance (in centimeters) they were from the center of the target in their last shot. Archer A was $3\ cm$ away, archer B was $4\ cm$ away and archer C was $6\ cm$ away. How many arrows does each one receive?

A group of three friends, Sarah, Luke and Ava, have set up a lemonade stand at the neighborhood festival. To start, Sarah contributed $10\ \$$, Luke $15\ \$$ and Ava $25\ \$$. At the end of the day they have made a net profit of $160\ \$$. If they decide to share the profits directly proportionally to the money each one put in at the beginning, how much money will each of the three friends take?

A box with $120$ tickets for a music festival is to be shared among three local middle schools. The share will be done inversely proportionally to the number of students who arrived late on the last cultural day. School "A" had $10$ late arrivals, School "B" had $15$ late arrivals and School "C" had $30$ late arrivals. How many tickets will each school receive?

Three friends from an e-sports club have won a regional tournament and are going to share a prize of $\$1\,900$. The share must be directly proportional to the points obtained in the grand final. The first player got $150$ points, the second $120$ points and the third $110$ points. However, before collecting, the club deducts $5\%$ of the total prize for administration fees. What net amount will each of the three players receive after applying the deduction and calculating the proportional shares?

A sustainable courier company wants to reward its three best delivery riders from the bicycle section. The total prize is $\$1\,160$ and will be shared inversely proportionally to the number of packages that arrived late during the last month. Courier $A$ had $2$ late deliveries, courier $B$ had $3$ and courier $C$ had $4$. Work out how much money each one receives.

Three families have rented a cabin to spend Spring Break. The total cost of the rent is $\$1\,500$. They decide to share the cost directly proportionally to the number of nights each family has stayed in the cabin. The Miller family stayed $5$ nights, the Johnson family stayed twice as many nights as the Smith family, and the Smith family stayed $3$ nights fewer than the Miller family. What amount must each family pay?

A music app has shared its quarterly profits among three emerging artists directly proportionally to the number of streams of their songs. We know that artist $X$ received $\$1\,200$ for having $300\,000$ streams. If artist $Y$ had $450\,000$ streams and artist $Z$ received $\$2\,400$, calculate:

1. The number of streams that artist $Z$ had.

2. The amount of money that artist $Y$ received.

3. The total profit that the app shared among the three.

A grandfather wants to share a collection of $165$ old coins among his three grandchildren inversely proportionally to their ages, which are $12, 15$ and $20$ years old. The youngest grandchild is so excited that the grandfather decides to give him, in addition, $10$ more coins that he takes from his own personal reserve. How many coins will each grandchild end up with?

An inheritance of $\$112\,000$ is shared among three charities directly proportionally to the places they offer. Charity $P$ has $x$ places, charity $Q$ has three times as many places as $P$, and charity $R$ has half as many places as $Q$. Knowing that charity $Q$ has received $\$60\,000$, how much money does each of the other two charities receive?

In a recycling competition, a city council shares a fund of $\$2\,600$ among three schools inversely proportionally to the number of tons of unrecycled waste they have generated. School $1$ generated $\frac{1}{2}$ ton, School $2$ generated $\frac{1}{3}$ of a ton and School $3$ generated $\frac{1}{4}$ of a ton. What financial prize does each school receive?

A rectangular plot of $1\,200$ $m^2$ is divided into three school garden plots for the 7th grade classes. The share of the area is done directly proportionally to the number of students in each class. In class $A$ there are $24$ students, in class $B$ there are $28$ students and class $C$ has a number of students such that they have been allocated $450$ $m^2$ of garden plot.

1. How many students does class $C$ have?

2. What area corresponds to classes $A$ and $B$?