Question 80665
QUESTION:


The difference of two numbers is 33. The second is 7 less than 3 times the first. What are the two numbers?


ANSWER:


Let us assume that one number is x.


Three times of x can be written as 3x.


7 less than 3 times the first can be written as 3x - 7.



Then we can take the other number as  3x - 7.


It is given that their difference is 33.



So we can write, first number -second number = 33


That is x - (3x-7) = 33



==> x - 3x + 7 = 33 ( remove the parenthesis by multiplying each term inside it with -1.)



==> -2x + 7 = 33. ( x - 3x = -2x)


Subtract 7 from both sides of the equation.  Then we have,



-2x + 7 - 7 = 33 - 7 



==> -2x = 26


Now divide both sides of the equation by -2.



==> -2x/-2 = 26/-2



==> x = -13.



So the first number is -13.


We have second number = 3x - 7


= 3(-13) - 7


= -39 - 7


= -46.


So the numbers are -13 and -46.



To check the answer....find the difference of these numbers.



That is -13 - (-46) = -13 + 46 = 33.That is our answer is correct.



Hope you understood.


Regards.


Praseena.