Question

the ratio of the difference obtained by subtracting 2 from thrice a number to the sum of twice the same number and 5 is 13:15. what is the number

Answer 1

Let the number in question be x

Write down the two sets of the algebraic expressions: 

i) Difference obtained by subtracting 2 from thrice a number 

= 3x - 2

ii) Sum of twice the number and 5

= 2x + 5

Get the ratio of the two algebraic expressions = 13:15

3x-2:2x+5 = 13:15

Meaning: 

3x-2/2x+5= 13/15

cross multiply as follows: 

13(2x+5) = 15( 3x-2)

26x+65 = 45x -30

45x-26x = 65+30

19x = 95

x= 5

Therefore the number is 5

Answer 2

Let the number be 'x'
The thrice of the number is 3x
The twice of the number is 2x
Difference obtained by subtracting 2 from thrice of the number is 3x-2
Sum of twice the number and 5 is 2x+5
3x-2 : 2x+5 = 13:15
After multiplication, we get
=> 13(2x+5)=15(3x-2)
=> 26x+65=45x-30
=> 45x-26x=65+30
=> 19x=95
=> x=5
The number is 5
Hope it helps.