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?

Question

5255 views around the world

You can reuse this answer
Creative Commons License

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