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Simplify: 2a – [3b – {a – (2c – 3b) + 4c3(a – b 2c)}].
Given equation: 4a – [6b – {a – (2c – 2b) + 4c+ 3(a – b 2c)}]
= 4a – [6b – {a – 2c + 2b + 4c+ 3a – 3b – 6c}]
= 4a – [6b – {a + 3a – 2c + 4c – 6c +2b – 3b}]
= 4a – [6b – {4a – 4c– b}] = 4a – [6b –4a + 4c + b]
= 4a – [7b – 4a + 4c] = 4a – 7b + 4a – 4c
= 8a – 7b – 4c
5x – [2y – {7x – (3z y) + 2z – 3(x +3y z)}] =
Given expression: 5x – [2y – {7x – (3z y) + 2z – 3(x +3y z)}]
= 5x – [2y – {7x – 3z + y + 2z – 3x – 9y + 3z}]
= 5x – [2y – {7x – 3x – 3z + 2z + 3z + y – 9y}]
= 5x – [2y – {4x + 2z – 8y}]
= 5x – [2y – 4x – 2z + 8y]
= 5x – [10y – 4x – 2z]
= 5x – 10y + 4x + 2z
= 9x – 10y + 2z
When Rohan multiplies a certain number by 13 and adds 4 to the product, he gets 173. Find the number.
Let the number be x
When x multiplied by 13 = 13x
When 4 added to 13x = 13x+4
Final result Rohan got = 173
Putting these together,
13x+4 = 173
13x = 173 – 4 = 169
x = = 13
So the required number is 13.
Write the following using numbers, literals and signs of basic operations:
The sum of quotient of 7 by 3 and x.
The quotient of 7 by 3 =
Sum of x and = +x
So, the given statement can be written as +x.
Think of a number. Multiply by 3. Add 7 to the result. Subtract y from this result. What is the result?
Consider x as the number.
Multiplying the number by 3 = 3x
Again add 7 to the number = 3x + 7
By subtracting y from the above equation = 3x + 7 – y.
Hence, the result is 3x + 7 – y.
The number of people living on the ground floor of a building is 12 less than the twice of the number of people on first floor. If the first floor has x number of people, how many numbers of people does the ground floor has?
Consider y as the number of people on the ground floor
We know that
The number of people on the first floor = x
It is given that number of people on the ground floor of a building is 12 less than the twice of the number of people on first floor
So, we get
y = 2x – 12
Hence, the number of people on the ground floor is 2x – 12.
Shivani spend Rs a per week and saves Rs b per day. What is her income for two weeks?
Amount spent per week = Rs a
Amount saved per day = Rs b
Amount saved in one week = 7b
So, the total income for one week = Amount spent per week + Amount saved per week
Substituting the values
Total income for one week = a + 7b
We get income for 2 weeks = 2 (a + 7b) = Rs 2a + 14b
Hence, the income of Shivani for two weeks is Rs 2a + 14b.
Sandeep scores 70 marks in English and x marks in Hindi. What is his total score in the two subjects?
Marks scored by sandeep in English = 70
Marks scored by sandeep in Hindi = x
So, the total scores in the two subjects = x + 70
Hence, the total score of Sandeep in two subjects is x + 70.
One pen weigh 15 grams and one pencil weighs 10 grams. Determine the weight of x pens and y pencils.
Weight of one pen = 15 g
Weight of one pencil = 10 g
So, the weight of x pens = 15x g
So, the weight of y pencils = 10y g
We get the weight of x pens and y pencils = (15x + 10y) g
Hence, the weight of x pens and y pencils is (15x + 10y) g.
a² × 2ab³ x 3ab is equal to
It can be written as,
2 × a² × a × a × b³ × b = 2a³b³
In a room there are 2x² rows of chairs and each row contains x²/2 chairs. The total number of chairs in the room is
We know that
Total number of chairs in the room = Number of rows × Number of chairs in each row.
By substituting the values,
Total number of chairs in the room = 2x² × = x⁴
If 3x²y and 3xy² denote the length and breadth of a rectangle, then its area is
We know that area of a rectangle = length × breadth
By substituting the values
Area = 3x²y × 3xy² = 9x³y³
4a²b⁴ × 2a³b² × 6a²b is equal to
It can be written as
4a²b⁴ × 2a³b² × 6a²b = 4 × 2 × 6 × a² × a³ × a² × b⁴ × b² × b = 48a⁷b⁷
a²b³ × 2ab² is equal to
It can be written as
a²b³ × 2ab² = 2a² × a × b³ × b² = 2a³b⁵.
The product of x and y added to the quotient of x by y is written as
The product of x and y = xy
The quotient of x by y =
Both added together = xy+
The product of x and y added to quotient of x by y is xy+
6 apple taken away from the sum of x Apples and y Apples is
Sum of x Apples and y Apples= x+y
6 Apples taken away from x+y Apples = x+y6
6 Apples taken away from the sum of x and y Apples is x+y6 Apples.
The quotient of x by 5 is multiplied by 3y is written as
Quotient of x by 5 =
multiplied by 3y = × 3y =
So, it can be written as
The quotient of x by 5 is added to 3 is written as
Quotient of x by 5 =
added to 3 = + 3
The quotient of x by 5 is added to 3 is written as + 3.
7 less than twice a number x is written as
Let a number be x.
Twice the number x = 2x
7 less than 2x = 2x7
So, 7 less than twice a number x is written as 2x – 7.
If there are x rows of flower pots and each row contains x² pots. Determine the total number of flower pots.
Number of rows of flower pots = x
Each row contains = x² pots
So, the total number of pots = number of rows of flowers × pots in each row
We get,
Total number of flower pots = x × x² = x³
Hence, the total number of flower pots is x³