Proportional sharing
Three partners invest different amounts of capital, for different lengths of time, in a business. When sharing out the profit, it is not enough to divide by three: you have to share fairly, according to what each one has put in. That is proportional sharing, and in 4th ESO it can depend on two criteria at once.
Revision: direct and inverse sharing
Divide the number $4500$ in direct proportion to $2$, $3$ and $4$.
Divide the number $4500$ in direct proportion to $2$, $3$ and $4$.
Divide the number $3900$ in inverse proportion to $2$, $3$ and $4$.
Divide the number $3900$ in inverse proportion to $2$, $3$ and $4$.
Sharing with fractions or decimals
When the parts are given as fractions, it is best to reduce them to a common denominator before adding.
Divide $620$ in direct proportion to the fractions $\frac{1}{2}$, $\frac{1}{3}$ and $\frac{1}{5}$.
Divide $620$ in direct proportion to the fractions $\frac{1}{2}$, $\frac{1}{3}$ and $\frac{1}{5}$.
Divide the number $3420$ into parts in direct proportion to $1,2$, $0,8$ and $2,5$, and in inverse proportion to $\frac{3}{4}$, $\frac{1}{2}$ and $\frac{5}{2}$.
Divide the number $3420$ into parts in direct proportion to $1,2$, $0,8$ and $2,5$, and in inverse proportion to $\frac{3}{4}$, $\frac{1}{2}$ and $\frac{5}{2}$.
We want to divide $9300$ € into parts in inverse proportion to the decimals $0,4$, $0,5$ and $0,8$. Calculate the amount corresponding to each share.
We want to divide $9300$ € into parts in inverse proportion to the decimals $0,4$, $0,5$ and $0,8$. Calculate the amount corresponding to each share.
Two criteria at once: direct and inverse combined
Sometimes the sharing depends on two different things, one directly and the other inversely.
A grandfather decides to share $8600$ € among his three grandchildren in direct proportion to their average grades ($7,5$, $8,0$ and $6,0$) and in inverse proportion to…
A grandfather decides to share $8600$ € among his three grandchildren in direct proportion to their average grades ($7,5$, $8,0$ and $6,0$) and in inverse proportion to their ages ($15$, $16$ and $12$ years). How much does each receive?
In a company, a productivity bonus of $12400$ € is shared among three employees in direct proportion to their years of service ($4$, $5$ and $8$ years) and in inverse…
In a company, a productivity bonus of $12400$ € is shared among three employees in direct proportion to their years of service ($4$, $5$ and $8$ years) and in inverse proportion to their days of absence ($2$, $3$ and $4$ days). Calculate the share allocated to each employee.
An alloy of $420$ grams is composed of gold, silver and copper. The masses of these metals in the alloy are directly proportional to the numbers $3$, $4$ and $5$, and…
An alloy of $420$ grams is composed of gold, silver and copper. The masses of these metals in the alloy are directly proportional to the numbers $3$, $4$ and $5$, and inversely proportional to their relative densities, which are approximately $19$, $10$ and $9$ respectively. Set up the division and determine how many grams of each metal are in the alloy (express the result rounded to two decimal places).
Algebraic approach
When a piece of data is missing (a share, a total, an unknown number), you set up an equation using the constant of proportionality $k$.
A sum of money of $30000$ € is divided into three parts in direct proportion to $x$, $x+2$ and $x+4$. If the largest share obtained is $12000$ €, set up an equation to…
A sum of money of $30000$ € is divided into three parts in direct proportion to $x$, $x+2$ and $x+4$. If the largest share obtained is $12000$ €, set up an equation to determine the value of $x$ and calculate the other two shares.
An amount of money is divided in direct proportion to $3$, $5$ and $k$. Knowing that the second share corresponds to $1500$ € and the total amount shared is $4200$ €,…
An amount of money is divided in direct proportion to $3$, $5$ and $k$. Knowing that the second share corresponds to $1500$ € and the total amount shared is $4200$ €, find the value of the parameter $k$ and calculate the amounts of the first and third shares.
Back to the start: to share the profit fairly when capital and time both vary, multiply the capital contributed by the number of months each partner stayed in; the total profit is shared in direct proportion to that product.