PROBLEMS ON TRANSLATING VERBAL PHRASES TO ALGEBRAIC EXPRESSIONS

To translate words into an algebraic expression or equation, write the numbers and operations in the order they appear (working from left to right)

Problem 1:

5 more than 6 times a number

Solution :

Let the number be x.

6 times a number = 6x

5 more than 6 times a number = 6x + 5

Problem 2 :

8 less than a number, divided by 3

Solution :

Let the number be x.

A number divided by 3 = x/3

8 less than a number, divided by 3 = x/3 - 8

Problem 3 :

8 times the cube of a number

Solution :

Let the number be x.

8 times the cube of a number = 8x³

Problem 4 :

The sum of the square of a number and 4

Solution :

Let the number be x.

The sum of the square of a number and 4 = x² + 4

Problem 5 :

10 times the sum of a number and 9

Solution :

Let the number be x.

The sum of a number and 9 = x + 9

10 times the sum of a number and 9 = 10(x + 9)

Problem 6 :

18 fewer than half of a number

Solution :

Let the number be x.

Half of a number = x/2

18 fewer than half of a number = (x/2) - 18

Problem 7 :

The quotient of 8 and twice a number

Solution :

Let the number be x.

The quotient of 8 and twice a number = 8/2x

Problem 8 :

2 subtracted from the square of a number

Solution :

Let the number be x.

The square of a number = x²

2 subtracted from the square of a number = x² - 2

Problem 9 :

Twice the quantity of number decreased by seven

Solution :

Let the number be x.

Twice the quantity of number decreased by seven = 2x - 7

Problem 10 :

The sum of three times the quantity of a number increased by six and half the same number.

Solution :

Let the number be x.

= 3(x + 6) + (1/2)x

Problem 11 :

A quarter of the square of a number

Solution : 

Let the number be x.

A quarter of the square of a number = x²/4

Problem 12 :

12 divided by the difference of a number and 2

Solution :

Let the number be x.

The difference of a number and 2 = x - 2

12 divided by the difference of a number and 2 = (x - 2)/12

Problem 13 :

The sum of 4 times a number and that same number cubed.

Solution :

Let the number be x.

The sum of 4 times a number and that same number cubed = 4x + x³

Problem 14 :

The product of the quantity x plus y and the quantity x minus y

Solution :

Quantity x plus y = x + y

Quantity x minus y = x - y

The product of the quantity x plus y and the quantity x minus y

= (x + y) (x - y)

Problem 15 :

If Rohit has 5xy toffees and Shantanu has 20 yx toffees, then Shantanu has _____ more toffees.

Solution :

Number of toffees Rohit has = 5xy

Number of toffees Shantanu has = 20xy

= 20xy - 5xy

= 15 xy

Shantanu has 15xy more toffees than Rohit.

Problem 16 :

The unlike terms in perimeters of following figures are___________ and __________.

Solution :

Length = 2x, width = y

Perimeter of rectangle = 2(length + width)

= 2(2x + y)

= 4x + 2y

Problem 17 :

Solution :

Length = x, width = y²

Perimeter of rectangle = 2(length + width)

= 2(x + y²)

Problem 18 :

If (x²y + y² + 3) is subtracted from (3x²y + 2y² + 5), then coefficient of y in the result is ________.

Solution :

= (3x²y + 2y² + 5) - (x²y + y² + 3)

= 3x²y + 2y² + 5 - x²y - y² - 3

= 3x²y - x²y + 2y² - y² + 5 - 3

= 2x²y + y² + 2

Problem 19 :

Like terms in the expression n(n + 1) + 6 (n – 1) are ___________and ________.

Solution :

= n(n + 1) + 6 (n – 1)

=  n² + n + 6 n – 6

n and 6n are like terms.

Problem 20 :

The length of a side of square is given as 2x + 3. Which expression represents the perimeter of the square?

(a) 2x + 16      (b) 6x + 9      (c) 8x + 3      (d) 8x + 12

Solution :

Side length of square = 2x + 3

Perimeter of square = 4(side length)

= 4(2x + 3)

= 8x + 12

So, option d is correct.

Problem 21 :

The value of 3x² – 5x + 3 when x = 1 is

(a) 1     (b) 0     (c) –1     (d) 11

Solution :

Given that, 3x² – 5x + 3

Applying x = 1, we get

= 3(1)² – 5(1) + 3

= 3 - 5 + 3

= 6 - 5

= 1

Problem 22 :

The side length of the top of square table is x. The expression for perimeter is:

(a) 4 + x      (b) 2x      (c) 4x       (d) 8x

Solution :

Side length of square = x

Perimeter of square = 4x

So, option c is correct.