A number 84 is divided into two parts. if the difference between half of the first part and one-third of the second part is 12, find two parts of number.
Call the first part A
Call the second part B
We know that A + B = 84
and that A/2 – B/3 = 12
From there it's just substitution A = 84 – B above, where it says A we're going to plug this in
(84 – B)/2 – B/3 = 12
Let's multiply everything by 6 and
get rid of those pesky denominators 3 • (84 – B) – 2 • B = 6 • 12
252 – 3B – 2B = 72
Combine like terms 252 – 5B = 72
Subtract 252 from both sides –5B = –180
Divide both sides by –5 B = 36
Plug this 36 back into the original equation A + 36 = 84
A = 84 – 36
A = 48
We could have solved for A first; it doesn't matter.
Just remember which one you designated as "the first part"
so you know which one to divide by 2 and which one to divide by 3.
.
