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;

$\frac{3}{5}=\frac{3x}{y}$ ..................... Let first perso's amount is 3x and find second person's amount in terms of x.

$\frac{5}{3}\times \frac{3}{5}=\frac{5}{3}\times \frac{3x}{y}$ ......................... Multiply both sides with $\frac{5}{3}$.

$1=\frac{5x}{y}$

$y=5x$.

$3x+5x=\mathrm{\$}1400}$ ....................... Equate given sum.

$8x=\mathrm{\$}1400}$

$x=\mathrm{\$}\frac{1400}{8}}$ ........................... Divide both sides by 8.

$=\mathrm{\$}175}$

$3x=3\times 175$ ............................... Substitute $x=\mathrm{\$}175}$.

$=\mathrm{\$}525}$

$5x=5\times 175$

$=\mathrm{\$}875}$

Hence, the each person ed in the question will receive $525 and $875.