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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

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  • $\begingroup$ 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. $\endgroup$ – AD. Nov 13 '10 at 20:41
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-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

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  • $\begingroup$ thank you! cause of confusion - 1 @%$ multiplication error $\endgroup$ – Frank Nov 13 '10 at 20:21
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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.

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

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