Question 80685
QUESTION:

one number is 5 more than another number. Four times the larger number plus 3 times the smaller is 97. Find the numbers.


ANSWER:


Assume that one number is  = x


Then the other number is = x + 5



Here the larger number is x + 5



Four times the larger number is = 4(x+5)


Here the smaller number is = x



Three times the smaller number is = 3x


Four times the larger number plus 3 times the smaller is =  97


==> 4(x+5) + 3x = 97



==> 4x + 20 + 3x = 97



==> 4x+ 3x + 20 = 97



==> 7x + 20 = 97



subtract 20 from both sides of the equation



==> 7x + 20 - 20 = 97 -20



==> 7x = 77


Divide both sides of the equation by 7



==> 7x/7 = 77/7



==> x = 11.


So the first number is 11


Then the other number, which is 5 more than that of first = 11+ 5= 16


The second number is 16.



To check the answers....it is given that...Four times the larger number plus 3 times the smaller is 97


That is 4*16 + 3*11 = 64 + 33 = 97.


That is our answer is correct.



Hope you understood.



Regards.


Praseena.