Formula Sheet: Finding the Unknown

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.

M(n) is the number of matchsticks at position n. This formula describes how matchstick patterns grow linearly as n increases.

h is height, and w is weighted height. This equation illustrates that height increases by 1 unit as weight changes.

x, y, and z represent weights. When added, the total weight must equal the weight on the opposite side of a scale.

This method involves substituting values into an equation until the left-hand side (LHS) equals the right-hand side (RHS).

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.

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.

This equation form helps to isolate x, allowing one to find unknowns across various applications by rearranging terms.

Letting k represent the nth step in a sequence, solving the equation provides the step number that uses a specific number of tiles.

This equation relates distance traveled to speed and time taken, aiding in solving movement-related problems.

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.

Here, y represents an unknown weight, and solving this equation allows one to find the individual weight based on the total.

This basic equation represents a direct calculation to isolate x, ensuring that x can be found easily through division.

This equation helps find the unknown number of marbles when one person has more than the total of the other.

Here, p is the number of people; solving this determines how many can be served given fixed costs and total budget.

This equation will yield the value of x after subtracting terms to find the unknown in a structured balance.

In this equation for n, isolating helps determine the unknown factor via rearranging and simplifying the expression.

After performing operations to isolate x, we determine what x must be to fulfill this equation.

This equation asks for the value of n that satisfies the predetermined relationship in a sequence setting, showing solution patterns.

This rearranged equation shows how to balance terms involving x, enabling isolation and calculation of its value.