The sum of two numbers is 30 and their difference is 12.what are the 2 numbers?

1 Answer
Apr 10, 2018

The two numbers are #21# and #9#

Explanation:

Let the two numbers be #a# and #b#

The sum of these numbers is #30#
#a + b = 30#

The difference between these numbers is #12#
#a - b = 12#

#color(white)(mmmmmmmm)#―――――――――

I.  You can solve this by logic.

If the two numbers were exactly equal, then they would both be #15#.
#15 + 15 = 30#

But the difference would be #0#, not #12#

So if you lowered #b# by one point, and added that to #a#, then the two numbers would be #16# and #14#, and the difference would be #2#.

So you can see that for every point you subtract from #b# to add to #a#, you increase the distance between them by #2#

So, by logic, you need to subtract #6# points from #b# and add them to #a# to create a difference of #12#

#(15 + 6)# minus #(15 - 6)# gives a difference of #12#
#color(white)(.m)21 color(white)(.....) - color(white)(mmnn)9        =   12#

Answer:
The two numbers are #21# and #9#

#color(white)(mmmmmmmm)#―――――――――

II.  You can solve this by math

These are simultaneous equations, so you can solve them by math.

#color(white)(.)a + b = 30#
#color(white)(.)a - b = 12#
#color(white)()#――――――
#2acolor(lightgray)( + 0)=42#
#color(white)(.)##a          = 21# #larr# same answer