The sum of a number and two times a smaller number is 62. Three times the bigger number exceeds the smaller number by 116. The bigger and smaller number is what?

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Answer 1 · 2018-07-28T10:50:53

The bigger and smaller numbers are #42 and 10 # respectively.

Let the bigger and smaller number be #b and s # respectively.

By given conditions , # b+2 s=62 ; (1) and 3 b-s=116 ; (2)#

multiplying the equation (2) by #2# we get, # 6 b -2 s =232; (3)#

Adding equations (1) and (3) we get,

# (b+cancel(2 s)) + (6 b-cancel(2 s))=62+232# or

#7 b = 294 or b= 294/7 or b= 42# ,putting #b=42# in

equation (1) we get , # 42 +2 s=62 :. 2 s = 62-42 # or

#2 s =20 or s =10 :. b=42 and s=10#

The bigger and smaller numbers are #42 and 10 # [Ans]

Answer 2 · 2018-07-28T12:06:29

#x = 10 #
#y = 42 #

The sum of a number and two times a smaller number is 62
#2x + y = 62#
so # y = 62 - 2x #

Three times the bigger number exceeds the smaller number by 116
#x +116 = 3y#

substitute for #y#:
#x +116 = 3(62 - 2x)#
#x +6x = 186 -116#
#7x = 70 #
#x = 10 #

#3y = 10 +116 = 126#
#y = 126/3 = 42