The difference of two numbers is 3. Their sum is 13. How do you find the numbers?

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Answer 1 · 2017-01-06T04:35:53

The two numbers are #8# and #5#.

Consider the two numbers as #x# and #y#. From the given data, we write:

#x-y=3#
#x+y=13#

From the first equation, we determine a value for #x#.

#x-y=3#

Add #y# to both sides.

#x=y+3#

In the second equation, substitute #x# with #color(red)((y+3))#.

#x+y=13#

#color(red)((y+3))+y=13#

Open the brackets and simplify.

#color(red)(y+3)+y=13#

#2y+3=13#

Subtract #3# from each side.

#2y=10#

Divide both sides by #2#.

#y=5#

In the first equation, substitute #y# with #color(blue)(5)#.

#x-y=3#

#x-color(blue)(5)=3#

Add #5# to each side.

#x=8#