Finding the Unknown – Formula & Equation Sheet
Essential formulas and equations from Ganita Prakash II, tailored for Class 7 in Mathematics.
This one-pager compiles key formulas and equations from the Finding the Unknown chapter of Ganita Prakash II. Ideal for exam prep, quick reference, and solving time-bound numerical problems accurately.
Formulas
Weight Balance: a + b = c + d
a, b, c, and d represent weights on a balance scale. This formula indicates that weights on either side of a balance scale are equal when arranged correctly.
Matchstick formula: M(n) = 2n + 1
M(n) is the number of matchsticks at position n. This formula describes how matchstick patterns grow linearly as n increases.
Equation of heights: h = w + 1
h is height, and w is weighted height. This equation illustrates that height increases by 1 unit as weight changes.
Equation for finding unknown weights: x + y = z
x, y, and z represent weights. When added, the total weight must equal the weight on the opposite side of a scale.
Trial and Error Method: If LHS = RHS, then x is the solution
This method involves substituting values into an equation until the left-hand side (LHS) equals the right-hand side (RHS).
Cost Equation: Total Cost = Cost per Plate × Number of Plates + Delivery Charge
Represented as C = P × N + D, where C is total cost, P is cost per plate, N is number of plates, and D is delivery charge.
Savings Equation: J = S + 650m and S = 5050 + 500m
J represents Jahnavi's savings, S represents Sunita's savings, and m is the number of months. This system shows how savings accumulate over time.
Linear Equation: Ax + B = Cx + D
This equation form helps to isolate x, allowing one to find unknowns across various applications by rearranging terms.
Finding the unknown in a sequence: 3k + 1 = 100
Letting k represent the nth step in a sequence, solving the equation provides the step number that uses a specific number of tiles.
Average speed formula: Total Distance = Speed × Time
This equation relates distance traveled to speed and time taken, aiding in solving movement-related problems.
Equations
2e = 6
In this equation, e denotes the weight of an egg. Solving gives the weight of a fried egg when there are three eggs totaling six.
4 + 2y = 16
Here, y represents an unknown weight, and solving this equation allows one to find the individual weight based on the total.
5x = 11
This basic equation represents a direct calculation to isolate x, ensuring that x can be found easily through division.
x + 30 = 60
This equation helps find the unknown number of marbles when one person has more than the total of the other.
450 = 25p + 50
Here, p is the number of people; solving this determines how many can be served given fixed costs and total budget.
6x + 9 = 66
This equation will yield the value of x after subtracting terms to find the unknown in a structured balance.
3n = 10 + n
In this equation for n, isolating helps determine the unknown factor via rearranging and simplifying the expression.
x - 3 = 24
After performing operations to isolate x, we determine what x must be to fulfill this equation.
2n + 1 = 99
This equation asks for the value of n that satisfies the predetermined relationship in a sequence setting, showing solution patterns.
4x - 9x = 3
This rearranged equation shows how to balance terms involving x, enabling isolation and calculation of its value.
