Algebra helps convert business statements into mathematical form so we can solve for unknowns like price, quantity, cost, profit, demand, and break-even level.
Typical exam uses:
A linear equation in one variable has the form: ax + b = 0 (a ≠ 0)
Solution idea: isolate x.
Example: 3x + 15 = 0 ⇒ 3x = −15 ⇒ x = −5
A linear equation in two variables: ax + by = c.
To find unique values of x and y, we need two independent equations.
Example: 2x + y = 11 x + y = 7 Subtract second from first: x = 4, then y = 3.
If 2 notebooks + 1 pen cost ₹110 and 1 notebook + 1 pen costs ₹70: 2N + P = 110 N + P = 70 Subtract → N = 40, then P = 30.
A quadratic equation has the form: ax^2 + bx + c = 0 (a ≠ 0)
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5x − 3 = 22 ⇒ 5x = 25 ⇒ x = 5. So, x = 5.
To solve simultaneous linear equations, we can use elimination.
Example: 2x + y = 11 x + y = 7
Subtract the second equation from the first: (2x + y) − (x + y) = 11 − 7 x = 4
Substitute x = 4 into x + y = 7: 4 + y = 7 ⇒ y = 3
Therefore, the solution is x = 4 and y = 3.
Business mathematics are mathematics used by commercial enterprises to record and manage business operations. Commercial organizations use mathematics in accounting, inventory management, marketing, sales forecasting, and financial analysis.
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Algebra helps convert business statements into mathematical form so we can solve for unknowns like price, quantity, cost, profit, demand, and break-even level.
Typical exam uses:
A linear equation in one variable has the form: ax + b = 0 (a ≠ 0)
Solution idea: isolate x.
Example: 3x + 15 = 0 ⇒ 3x = −15 ⇒ x = −5
A linear equation in two variables: ax + by = c.
To find unique values of x and y, we need two independent equations.
Example: 2x + y = 11 x + y = 7 Subtract second from first: x = 4, then y = 3.
If 2 notebooks + 1 pen cost ₹110 and 1 notebook + 1 pen costs ₹70: 2N + P = 110 N + P = 70 Subtract → N = 40, then P = 30.
A quadratic equation has the form: ax^2 + bx + c = 0 (a ≠ 0)
Quadratic formula: x = [−b ± √(b^2 − 4ac)] / (2a)
Discriminant (D): D = b^2 − 4ac
Quadratics occur when revenue/cost relationships create curved functions (e.g., profit with non-linear demand). Often we reject negative/irrational roots if not meaningful.
An inequality represents a range of possible values.
Examples:
Constraints like:
These are written using inequalities.
Break-even means profit = 0. So R = C. If R = pQ and C = F + vQ: pQ = F + vQ ⇒ (p − v)Q = F ⇒ Q = F/(p − v)
This is the same break-even logic you studied earlier, now expressed as algebra.
Many word problems reduce to linear equations after defining variables.
Steps (exam-friendly):
Common patterns:
Tip: After solving, substitute back into the original equation(s) to confirm.
If these notes helped you, a quick review supports the project and helps more students find it.
Break-even point is the level of sales/output at which profit is zero.
Profit Π = Revenue − Cost. At break-even, Π = 0, so Revenue = Cost.
If revenue R = pQ and cost C = F + vQ (fixed + variable), then: pQ = F + vQ (p − v)Q = F Q = F/(p − v)
This shows break-even units depend on fixed cost and contribution per unit (p−v).