The sum of two numbers is 30 and their difference is 20. What are the two numbers?

3 Answers
Oct 31, 2016

5 and 25

Explanation:

#x+x-20=30#
#2x-20 =30#
#2x -20 +20 = 30+20#
#2x = 50#

#x= **25**#

#x-20 = **5** #

#(x,y)=(25,5)#

Explanation:

Two numbers, x and y, have this relationship:

#x+y=30#

#x-y=20#

We can solve this - it's 2 equations with 2 unknowns. I'll take the second equation, solve for x, then substitute into the first one:

#x-y=20#

#x=20+y#

And so

#x+y=30#

#(20+y)+y=30#

#20+2y=30#

#2y=10#

#y=5#

We can now substitute this back into either starting equation - I'll do both to show that it works in both:

#x+y=30#

#x+5=30#

#x=25#

#x-y=20#

#x-3=20#

#x=25#

It all checks!

#(x,y)=(25,5)#

one number is #25# the other number is #5#

Explanation:

The problem asks for the identity of two unknown numbers.
This makes the problem one with two variables.
With two variables it is necessary to have two equations.

Let x be one number
Let y be the other number.

# x + y = 30 # ( the sum of the two numbers is 30 )
# x -y = 20# ( The difference of the two numbers is 20)

Solving the second equation for x

# x - y + y = 20 +y # This gives

# x = 20 + y #

Substituting this value into the first equation gives.

#20 + y + y = 30 # combining like terms and subtracting 20 gives

# 20 - 20 + 2y = 30 - 20# This gives

 #2y  =   10#    Dividing both sides by #2# to isolate #y# results in

# (2y)/2 = 10/2# solving this gives

#y= 5" "# Put the value of 5 for y into either equation to find x

# x + 5 = 30" "# subtract 5 from both sides.

# x + 5 -5 = 30 -5# resulting in

#x = 25#

The two unknown numbers are #5 and 25 #