The average of two numbers is 50. Their difference is 40, how do you write an equation that may be used to find x the smallest of the two numbers?

1 Answer
Aug 4, 2015

Answer:

#x=30#

Explanation:

You know that you need to find two numbers, #x# and let's say #y#.

The average of two numbers is equal to their sum divided by #2#, so your first equation will be

#(x+y)/2 = 50#

The difference between #y# and #x#, since #x# is the smallest of the two, is equal to #40#, which means that your second equation will be

#y - x = 40#

You thus have a system of two equations

#{( (x+y)/2 = 50), (y-x=40) :}#

To solve for #x#, use the first equation to express #y# as a function of #x#

#(x+y)/2 = 50 <=> x+y = 100 => y = 100 -x#

Plug this into the second equation to get

#(100-x) -x = 40#

#color(blue)(100 - 2x = 40)# #-># this is the equation that will get you #x#.

The value of #x# will be

#2x = 60 => x = color(green)(30)#

The value of #y# will be

#y = 100 - 30 = color(green)(70)#