# quick basic math equation question

I've got a solution to a economy class calculation, but I can't figure out how they came to the answer. Could you help me?

-5p + 80 = 8p +-50

.......? = ......?

120 = 12p

p = 10

Extra: do you know which rule they are using to get from the first line to the 3d?

Many thx

Math beginner, Frank

• I am glad if you understood this, the same idea/technique with perhaps a bit more complexity is frequently used to solve several kinds of mathematical problems. – AD. Nov 13 '10 at 20:41

-5p+80=8p-50

80=5p+8p-50

80=13p-50

80+50=13p

130=13p (to get 120=12p at this step, you can multiply both sides by 12/13, but it's not necessary to arrive at the final answer)

p=10

• thank you! cause of confusion - 1 @%$multiplication error – Frank Nov 13 '10 at 20:21 Add$5p+50$to both sides of the = sign, and then simplify each side. (If you wish you can do this in two steps: Add$5p$and then 50 to each side of the equality sign.) EDIT: The above leads to the equation$130 = 13p$which can be solved directly by dividing both sides of the equality sign by 13:$130/13 = 13p/13$, which after simplification gives us$10=p$-- which is the same as saying$p=10$. Note: To reach the equation$120=12p\$, that is contained in the original question, is not necessary in order to solve the equation.

• still don't get it - after the start I just end up with: 120 = 13p instead of 120 = 12p ..? what am I missing? – Frank Nov 13 '10 at 15:04
• You are missing that 80+50=130, not 120. – Ross Millikan Nov 13 '10 at 15:40
• many thanks - my bad for the multiplication error – Frank Nov 13 '10 at 20:20
• @Ross Millikan: You are right, fixed it. – AD. Nov 14 '10 at 5:15