#x# and #x+1# are two consecutive natural numbers. #1/4# of the larger exceeds #1/6# of the smaller by 1. What is the value of x?

2 Answers
Sunayan S
Mar 9, 2018

See below...

Explanation:

You have already given the numbers with variables. Then, we have to just calculate as per instruction.

  • #1/4# of the larger number is #color(red)(((x+1))/4#
  • #1/6# of the smaller number is #color(red)(x/6#

Then,

#(x+1)/4-x/6=1#

#=>(3x+3-2x)/12=1#

#=>x+3=12#

#=>x=9#

Hope it helps...
Tank you...

Sahar Mulla ❤
Mar 9, 2018

It is given that, #x# and #x+1# are two consecutive natural numbers. We, can conclude that #x+1# is the greater one.

#(1/4)^(th)# of the larger number, #=> color(red)(1/4(x+1)#

#(1/6)^(th)# of the smaller number, #=> color(magenta)(1/6(x)#

Now, combining these,
#color(red)((1/4)^(th) "of the larger number")# #" exceeds "# #color(magenta)((1/6)^(th) "of the smaller number")##" by " 1#

#=> color(red)(1/4(x+1)) = color(magenta)(1/6(x)) +1#

#=>3(x+1) = 2x+12#

#=> 3x+3 = 2x+12#

#=> x = 9#

The numbers would, hence, be # 9 and 10#

Verification;-

#1/4(10) = 5/2# #color(white)(ddddd)# and #color(white)(ddddd)# # 1/6(9)=3/2#

And, #5/2# exceeds #3/2# by 1 :)

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