WRITE AN PHRASE AS AN ALGEBRAIC EXPRESSION

Get the algebraic expressions in the following cases using variables, constants and arithmetic operations.

Problem 1 :

Subtraction of z from y.

Solution :

y - z

Problem 2 :

One-half of the sum of numbers x and y.

Solution :

= 1/2 of (x + y)

= (1/2)(x + y)

Problem 3 :

The number z multiplied by itself.

Solution :

= z ⋅ z

= z²

Problem 4 :

One-fourth of the product of numbers p and q.

Solution :

= (1/4) of p and q

= (1/4) (pq)

Problem 5 :

Numbers x and y both squared and added.

Solution :

Square of both,

= x² + y²

Problem 6 :

Number 5 added to three times the product of numbers m and n.

Solution :

= 5 + 3mn

Problem 7 :

Product of numbers y and z subtracted from 10.

Solution :

Product of y and z = yz

Subtracted from 10 = 10 - yz

So, the required algebraic expression is 10 - yz.

Problem 8 :

Sum of numbers a and b subtracted from their product.

Solution :

Sum of numbers a and b = a + b

their product = ab

= ab - (a + b)

= ab - a - b

So, the required algebraic expression is ab - a - b.

Problem 9 :

Arjun bought a rectangular plot with length x and width y and then sold a triangular part of it whose base is y and height is z. Find the area of the remaining part of the plot.

Solution :

Dimension of rectangle :

Length = x

Width = y

Dimension of triangle :

Base = y 

height = z

Area of remaining part = xy - (1/2)yz

Problem 10 :

Amisha has a square plot of side m and another triangular plot with base and height each equal to m. What is the total area of both plots?

Solution :

Side length of square plot = m

Base of triangular plot = m

height of plot = m

Total area = area of square plot + area triangular plot

= m² + (1/2) x m x m

= m² + (1/2) x m²

= m² + (m²/2)

= (2m² + m²)/2

= 3m²/2

Problem 11 :

A taxi service charges $8 per km and levies a fixed charge of $50. Write an algebraic expression for the above situation, if the taxi is hired for x km.

Solution :

Charge per km = $8

Fixed charge = $50

Distance to be covered = x km

Total cost = 8x + 50

Problem 12 :

Shiv works in a mall and gets paid $50 per hour. Last week he worked for 7 hours and this week he will work for x hours. Write an algebraic expression for the money paid to him for both the weeks.

Solution :

Cost per hour = $50

Number of hours worked last week = 7

Number of hours worked this week = x

Total number of hours = 7 + x

Amount to be paid both weeks = 50(7 + x)

Problem 13 :

Sonu and Raj have to collect different kinds of leaves for science project. They go to a park where Sonu collects 12 leaves and Raj collects x leaves. After some time Sonu loses 3 leaves and Raj collects 2x leaves. Write an algebraic expression to find the total number of leaves collected by both of them.

Solution :

Number of leaves Sonu collects = 12

Number of leave Sonu leaves = 3

Number of leaves Raj collects = x and 2x

= 12 - 3 + x + 2x

= 9 + 3x

Problem 14 :

A school has a rectangular play ground with length x and width y and a square lawn with side x as shown in the figure given below. What is the total perimeter of both of them combined together?

Solution :

Length = x and width = y

Side length of square = x

Perimeter of combined together = Perimeter of rectangle + perimeter of square

= xy + x(x)

= xy + x²

Problem 15 :

Find the perimeter of the figure given below

Solution :

Perimeter of rectangle = 2(length + width)

Length = 5x - y and width = 2(x + y)

= 2(5x - y + 2(x + y))

= 2(5x - y + 2x + 2y)

= 2(5x + 2x - y + 2y)

= 2(7x + y)