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Solved Example

Question: The sum of thrice the smaller is four times the larger, is 44. If one number is 4 more than another. What are the two numbers?
Solution:
Let x be the smaller number.

Then the larger number is 4 more = x + 4

The problem states,

3x + 4(x + 4) = 44

=> 3x + 4x + 16 = 44
 
=> 7x = 44 - 16

=> 7x = 28

=> x = 4

=> Smaller number = 4

and Larger number = 4 + 4 = 8
 

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Solved Examples

Question 1: Find the greatest common factor of 24, 40 and 60.
Solution:
Write the prime factorization of each given number

Factors of 24 = 2 × 2 × 2 × 3

Factors of 40 = 2 × 2 × 2 × 5

Factors of 60 = 2 × 2 × 3 × 5

=> GFC = 2 * 2 = 4

 

Question 2: If the area of a circle is 25 pi square feet, find its circumference.
Solution:
The area of circle is given by,

A = 25 pi square feet

We know, Area = pi × r × r.

and circumference = 2 x pi x r

Therefore,

pi × r × r = 25 pi

r × r = 25

=> r = 5 feet   ...................(1)

The circumference is,

2 × pi × r = 2 × pi × 5 = 10 pi feet

using equation (1)

=> Circumference of circle = 10 pi feet.
 

Question 3: A car moves at the speed of 81 km/hr. What is the speed of the car in meters per second?

Solution:
Speed of car = 81 km/hr

1 km = 1000 m

1 hr = 3600 sec

=> 81 km/hr = 81 x $\frac{1000}{3600}$ m/sec

= 81 x $\frac{5}{9}$ m/sec

= 45 m/sec

=> Speed of car = 45 m/sec.