Set up an equation, and solve the problem. A sum of $1400 is to be...

Step 1
An equation consists an equal symbol between two algebraic expressions that have the same value. The common algebraic equations in math consist of one or more variables. The solution for the variable should satisfy the equation.
Step 2
The given sum of $1400 is divided between two persons in the ratio $\frac{3}{5}$. It means that the ratio of amount of two persons is equal to $\frac{3}{5}$ . If let the amount of first person is 3x, then the amount for other person should be 5x as the ratio should be equal to $\frac{3}{5}$. Then equate the sum to $1400 and then find the amounts of each person as follows;
${\displaystyle \frac{3}{5}=\frac{3x}{y}}$ ..................... Let first perso's amount is 3x and find second person's amount in terms of x.
${\displaystyle \frac{5}{3}\times \frac{3}{5}=\frac{5}{3}\times \frac{3x}{y}}$ ......................... Multiply both sides with ${\displaystyle \frac{5}{3}}$.
${\displaystyle 1=\frac{5x}{y}}$
${\displaystyle y=5x}$.
${\displaystyle 3x+5x=\mathrm{\$}1400}$ ....................... Equate given sum.
${\displaystyle 8x=\mathrm{\$}1400}$
${\displaystyle x=\mathrm{\$}\frac{1400}{8}}$ ........................... Divide both sides by 8.
${\displaystyle =\mathrm{\$}175}$
${\displaystyle 3x=3\times 175}$ ............................... Substitute ${\displaystyle x=\mathrm{\$}175}$.
${\displaystyle =\mathrm{\$}525}$
${\displaystyle 5x=5\times 175}$
${\displaystyle =\mathrm{\$}875}$
Hence, the each person ed in the question will receive $525 and $875.