What are two numbers with a sum of 35 and a difference of 7?

1 Answer
Ken C.
Jul 15, 2016

Make a system of equations using the given information and solve to find the numbers are #21# and #14#.

Explanation:

The first thing to do in algebraic equations is to assign variables to what you don't know. In this case, we don't know either number so we'll call them #x# and #y#.

The problem gives us two key bits of info. One, these numbers have a difference of #7#; so when you subtract them, you get #7#:
#x-y=7#

Also, they have a sum of #35#; so when you add them, you get #35#:
#x+y=35#

We now have a system of two equations with two unknowns:
#x-y=7#
#x+y=35#

If we add them together, we see we can cancel the #y#s:
#color(white)(X)x-y=7#
#+ul(x+y=35)#
#color(white)(X)2x+0y=42#
#->2x=42#

Now divide by #2# and we have #x=21#. From the equation #x+y=35#, we can see that #y=35-x#. Using this and the fact that #x=21#, we can solve for #y#:
#y=35-x#
#->y=35-21=14#

So the two numbers are #21# and #14#, which do indeed add to #35# and have a difference of #7#.

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