Proportional Distributions

Divide the amount of $9\,000$ pesos in direct proportion to the numbers $2$, $3$ and $4$.

A grandfather decides to divide $2\,400$ pesos among his three grandchildren aged $8$, $10$ and $12$ in direct proportion to their ages. Determine the amount of money each receives.

Three partners, Nerea, Beatriz and Santiago, invest $15000$ pesos, $20000$ pesos and $25000$ pesos respectively to open a business. After one year, the company generates a net profit of $14400$ pesos. Calculate how much of the profit each partner receives if it is shared in direct proportion to the capital invested.

Divide the number $300$ into parts inversely proportional to $2$ and $3$.

In an athletics competition, the organisers share out a prize of $68\,000$ pesos in inverse proportion to the time taken by the top three finishers to cross the finish line. If they crossed the finish line in $12$, $15$ and $20$ minutes respectively, determine the cash prize awarded to each runner.

A grandmother wants to divide $84\,000$ pesos among her three grandchildren aged $10$, $12$ and $15$ years old. She hesitates between doing it directly proportional to their ages or inversely proportional to them. Calculate how much each grandchild would receive under both options and state which grandchild experiences the greatest absolute difference in money between the two methods.

Share $620$ shares in direct proportion to the fractions $\frac{1}{2}$, $\frac{1}{3}$ and $\frac{1}{5}$.

In a laboratory experiment, a $145$-gram sample of a chemical compound must be divided among three containers in inverse proportion to their temperatures. The temperatures are $\frac{1}{2}$ ºC, $\frac{2}{3}$ ºC and $\frac{3}{4}$ ºC. Calculate the exact amount of compound that will be placed in each container.

Divide the algebraic expression $N = 6x^2 + 8x$ directly proportional to the expressions $x$, $x+1$ and $x+3$. Express the three resulting parts in terms of $x$ and fully simplify the polynomials obtained.

Four workers paint a building. The first works $5$ days at a rate of $6$ hours per day; the second, $4$ days at $8$ hours per day; the third, $6$ days at $5$ hours per day and the fourth, $3$ days at $10$ hours per day. If they earn a total of $73\,600$ pesos and decide to share it in direct proportion to the total hours worked by each, find how much each worker will receive.

A productivity bonus of $50\,600$ pesos is shared among three factory employees. The distribution is carried out in direct proportion to their years of service in the company ($4$, $5$ and $8$ years) and in inverse proportion to the number of days absent during the year ($2$, $3$ and $4$ days). Calculate the bonus received by each employee.

A technology company shares $1\,000\,000$ pesos of profit among three departments in two phases. In the first phase, $40$% of the total is shared directly proportional to the overtime hours worked: $120$, $150$ and $130$ hours. In the second phase, the remaining $60$% is shared inversely proportional to the number of technical incidents reported: $2$, $4$ and $5$ incidents. Calculate the total final profit received by each of the three departments by combining both phases.

In a distribution directly proportional to the quantities $3$, $5$ and $7$, the first person receives $2\,400$ pesos. Calculate the total amount shared and what the other two people receive.

An amount of money has been divided in inverse proportion to the ages of three siblings, who are $10$, $15$ and $20$ years old. If it is known that the $15$-year-old sibling received $8\,000$ pesos, find the total amount shared and what the other two siblings receive.

An amount of $174\,000$ pesos has been divided inversely proportional to three unknown numbers $A$, $B$ and $C$. The amounts received were $80\,000$ pesos, $60\,000$ pesos and $34\,000$ pesos respectively. Knowing that the smallest of the three original numbers is $51$, determine the value of the other two numbers.