Expressions using Letter-Numbers – Formula & Equation Sheet
Essential formulas and equations from the Expressions using Letter-Numbers chapter of Ganita Prakash, tailored for Class 7 in Mathematics.
This one-pager compiles key formulas and equations from the Expressions using Letter-Numbers chapter of Ganita Prakash. Ideal for exam prep, quick reference, and solving time-bound numerical problems accurately.
Formulas
s = a + 3
s represents Shabnam's age, a is Aftab's age. This formula expresses Shabnam's age as 3 years more than Aftab's age, demonstrating how to represent real-world relationships with algebra.
a = s - 3
a is Aftab's age, s is Shabnam's age. This shows Aftab's age as 3 years less than Shabnam's, reinforcing the relationship of their ages.
Number of matchsticks = 2 × n
This formula calculates the number of matchsticks needed for 'n' L shapes, where each L is made of 2 matchsticks, illustrating direct proportionality.
Total cost = c × 35 + j × 60
c is the number of coconuts and j is the number of kgs of jaggery. This represents the total expenditure based on quantities of two items with fixed costs.
Perimeter of square = 4 × q
q stands for the side length of the square. This formula helps calculate the perimeter using the side length, common in geometry.
Total amount = 100x + 20y + 5z
Here, x, y, and z are counts of ₹100, ₹20, and ₹5 notes, respectively. This expression calculates total money based on different note denominations.
Time to grind y kg = 10 + 8y
This expression calculates the total time taken to grind 'y' kg of grain, showing the start-up time and processing time per kg.
Cost = 30x + 20y
x is the number of Jowar roti plates and y is the number of Pulao plates. This expression computes total money based on individual costs.
Distance covered in 3 weeks = 105 + 21z
z is the increase in distance per day. This formula represents total distance cycled over a period with linear increase.
Combined length = 20 + k
20 meters is the length of one pipe and k is the length of the additional pipe. This expression denotes the combined length for practical scenarios.
Equations
s = a + 3
Indicates the relationship between the ages of Shabnam and Aftab, useful for age-related problems.
a = s - 3
Rearrangement of the first equation, useful for finding Aftab's age given Shabnam's.
Total Revenue = 30x + 20y
Represents revenue from selling x plates of Jowar roti at ₹30 each and y plates of Pulao at ₹20 each.
Time = 10 + 8y
Equation to find the total time taken to grind y kg of grain, where initial startup time of 10 seconds is added to the grinding time.
Distance after 3 weeks: 105 + 21z
Equation for Radha's cycling distance over three weeks, accounting for both base distance and increase.
2 × n
Used to find the total number of matchsticks based on the number of L shapes created.
c × 35 + j × 60
Algebraic expression to compute the total expenditure on coconuts and jaggery.
Perimeter of square = 4 × q
This equation quantifies the perimeter of a square based on its side length q.
Total cash amount = 100x + 20y + 5z
Calculates total cash available from different denominations.
s = 2n
Defines the relationship for the number of matchsticks based on L shapes constructed.
