# Simple Examples That Show How to Solve the Equation for Profit

Making profits being the main goal of any business, assigns it a vital position in the field of economics. No business will run successfully without profit. Here are some examples that show how to solve the profit equation.

Prachi Patkar

Last Updated: Feb 14, 2019

Did You Know?

Every business enterprise invests some capital in order to succeed. Profit is thus termed as

**'ROI'**or**'return on investment'**. Conjugally, higher the ROI, higher is the investment.Profit Equation in Economics

Consider the equation given:

**f(x) = 7x +1**

Solving this equation for x=1

**f(1) = (7 * 1) + 1**

f(1) = 8

f(1) = 8

At every value of x, the value of f(x) will change.

The profit equation can be given in terms of functions as represented:

**P(x) = SP(x) - CP(x)**---------- Equation I

**Profit(x) = Selling Price(x) - Cost Price(x)**

**Profit(x) = Revenue(x) - Expenditure(x)**

Selling price can alternatively be termed as the revenue, and cost price can also be termed as the expenditure.

**Gross Profit = Direct Revenue - Direct Expenditure**

The equation containing indirect expenditures is called 'net profit equation'.

**Net Profit = Gross Profit + Indirect Incomes - Indirect Expenditures**

CP(x) = Variable costs + Fixed Costs

**P(x) = SP(x) - (Variable Cost + Fixed Cost)**---------- Equation II

Equation I and II are two formulas for solving profit equations.

Case I

**SP > CP**Value of P is positive

Positive value of P indicates that profit is incurred. Profit is maximum when the difference between SP and CP is maximum.

**SP < CP**Value of P is negative

Negative value of P indicates that loss has occurred. Loss is the highest when the difference between SP and CP is maximum.

Case III

**SP = CP**Value of P is zero

This indicates a no-gain and no-loss scenario.

Examples

**Problem I: (Based on equation I)**A book vendor buys three books of USD 5 each. He sells each of the book for USD 10. What is the profit?

**Solution:**Let us recall the formula for profit.

Profit = Selling Price - Cost Price

For one book: Profit = 10 - 5 = USD 5

For three books: Profit = USD 5 X 3 = USD 15 or Profit = (10 X 3) - (5 X 3) = 30 - 15 = 15

**Problem II: (Based on equation II)**Consider an ice cream stall which sells each ice cream at USD 8. The cost price of each ice cream is USD 6. The rent of the stall for a day is USD 10. Calculate the profit made if the stall sells 10 ice creams a day.

**Solution:**Writing the equations for selling and cost price functions.

SP(x) = (8 X 10) = 80

CP(x) = Fixed Cost + Variable Cost = 10 + (6 X 10) = 70

Substituting the values of SP(x) and CP(x) in equation II we get:

P(x) = SP(x) - CP(x) = 80 - 70 = 10

On sale of 10 ice creams, the profit made by the ice cream stall is USD 10.