With this pattern, we can easily find the number of matchsticks required in any number of squares.
Example: Find the number of matchsticks that will be used in pattern 32.
Sol: No. of matchsticks used in 1^{st } Pattern = 4
No. of matchsticks used in 2^{nd }Pattern = 8
No. of matchsticks used in 3^{rd } Pattern = 12
So, the pattern we observe here is = 4n, (n = 1, 2, 3, 4, ...)
Hence, no. of matchsticks that will be used in 32^{nd } Pattern = 4 x 32 = 128
Example: 2 + (9 – 3), (4 × 6) – 8
(4 × 6) – 8 = 24 – 8
= 16
Example: Find 3x – 12 if x = 6.
Sol: (3 × 6) – 12
= 18 – 12
= 5
Thus, 3x – 12 = 5.
Example: Write down the equation justify the given statement.
'The age of Riya is five more than three times the age of her son, where age of Riya is Q and her son is P.'
Sol: Given that,
Age of Riya's son = P
Age of Riya = Q
According to question, Riya's age (Q) is 5 more than three times the age of her son(P).
Hence, Riya's age , Q =5 + 3P.
Example: 8y+7y=?
8y
+7y
_______________
(8+7)y = 15y
_______________
Addition of −5x2+12xy and 7x2+xy+7x is shown below:
−5x^{2}+12xy
7x^{2}+xy+7x
______________
2x^{2}+13xy+7x
______________
Subtraction of −5x2+12xy and 7x2+xy+7x is shown below:
−5x^{2}+12xy
−7x^{2}+xy+7x
_____________
12x^{2}+11xy−7x
__________________
Thus, p = 2 × (l + b) or 2l + 2b, where, l and b are variable and the value of perimeter changes with the change in l and b.
To find the solution of the equation, we use the trial and error method.
Example: Find the value of x in the equation 25 – x = 15.
Sol: Here we have to check for some values which we feel can be the solution by putting the value of the variable x and check for LHS = RHS.
Let’s take x = 5
25 – 5 = 15
20 ≠ 15
So x = 5 is not the solution of that equation.
Let’s take x = 10
25 – 10 = 15
15 = 15
Here, LHS = RHS
Hence, x = 10 is the solution of that equation.
Q1: Write the algebraic expression for the statement 'Onefifth of a number x is subtracted from the sum of b and thrice of c'.
Sol: Sum of b and thrice of c = b + 3c.
One  fifth of x =
Required expression: b + 3c  .
Q2: Find the value of m in the given equation.
Sol:
Q3: The present age of Reena is 1/4 of her father’s age. If the present age of her father is 52 years, then what will be the age of Reena after 7 years? Finally, express the present ages of Reena and her father in ratio form.
Sol: Given that,
Present Age of Reena's Father = 52 years
∴ Present Age of Reena = (1/4) * Father's age
= (1/4) * 52
= 13 years
Reena's age after 7 years = Reena's present age + 7
= 13 + 7
= 20 years
Q4: The ratio of the present age of Sonam and Priya be 10 : 9. If sum of their ages be 57 years, then find their present ages respectively
Sol: Let's denote the present age of Sonam as 10𝑥.
And the present age of Priya as 9x, where x is a common multiplier.
A common multiplier is a number that can be multiplied by each term in a ratio or equation to produce equivalent ratios or equations.
In this context, the common multiplier refers to a number that can be multiplied by both parts of the ratio (in this case, the ages of Sonam and Priya) to maintain the same ratio relationship between them.
According to question,
10x+9x=57
19x=57 (Combining like terms)
Now, solve for x:
x = 57/19
x = 3
Now that we have found the value of 𝑥, we can find their present ages:
Sonam's age: 10x=10×3=30 years
Priya's age: 9x=9×3=27 years
So, Sonam's present age is 30 years, and Priya's present age is 27 years.
Q5: The breadth of a rectangular bed sheet is 5 m more than half the length of the bed sheet. What is the perimeter of the bed sheet, if the
length is x m?
Sol:
9 videos114 docs49 tests

1. What are matchstick patterns in algebra? 
2. How are variables used in common rules in geometry? 
3. What is the difference between a variable and a constant in algebra? 
4. How can we solve equations in algebra? 
5. How are algebraic expressions used in arithmetic operations? 

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