Proportional Distributions

Three friends, Alba, Beto and Caio, collaborated at a charity market selling crafts. They decide to share the $\$300$ profit directly proportional to the number of hours each worked: Alba worked $2$ hours, Beto $3$ hours and Caio $5$ hours. Calculate how much money each receives.

Three friends decide to rent a private server to play an online video game during the holidays. The total cost of the rental is $\$153$. They have agreed to share the payment directly proportional to the time each was connected: Álex was on for $12$ hours, Bea for $18$ hours and Cristian for $21$ hours. How much should each contribute to pay the bill?

A carpenter has a wooden strip of $240\text{ cm}$ and needs to cut it into three pieces whose lengths are proportional to the numbers $1$, $2$ and $3$. We call $k$ the length of the shortest piece, so that the other two measure $2k$ and $3k$. What will be the length of each piece?

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

A box containing $120$ tickets for a music festival is to be shared among three local secondary schools. The distribution will be made inversely proportional 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?

In a recycling competition, a municipality distributes a fund of $52\,000$ pesos among three schools in inverse proportion to the number of metric tons of non-recycled waste they generated. School $1$ generated $\frac{1}{2}$ metric ton, School $2$ generated $\frac{1}{3}$ of a metric ton, and School $3$ generated $\frac{1}{4}$ of a metric ton. What cash prize does each school receive?

Three families have rented a country house for the Easter holidays. The total cost of the rent is $30\,000$ pesos. They decide to share the expense in direct proportion to the number of nights that each family stayed in the house. The Sánchez family stayed $5$ nights, the Pérez family stayed twice as many nights as the García family, and the García family stayed $3$ nights fewer than the Sánchez family. How much must each family pay?

A donation of $110\,000$ pesos is shared among three charities in direct proportion 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 $Q$ received $60\,000$ pesos, how much money does each of the other two charities receive?

A rectangular plot of $1\,200$ $m^2$ is divided into three school vegetable gardens for 9th grade classes. The area is divided in direct proportion to the number of students in each class. Class $A$ has $24$ students, class $B$ has $28$ students, and class $C$ has a number of students such that it received $450$ $m^2$ of garden.

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

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

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

A grandfather wants to share a collection of $168$ antique coins among his three grandchildren in inverse proportion 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 taken from his own personal reserve. How many coins will each grandchild end up with?