help with cost price(CP) problem

May 2010
6
0
Hey Guys, i need detailed explanation of a few steps that i highlighted with red ink in the file, which you can find as an attachment.

1st and 2nd steps is about just the formula and executing it, and i'm fine with that ....

i need explanation with the 3rd step and the 4th step

Plz help me

Thank You :)
 

Attachments

May 2010
1,034
272
These are both standard algebra rearrangements.

Start from:
\(\displaystyle 30 = \frac{650 - CP}{CP} \times 100 \)

(multiply both sides by CP)
\(\displaystyle 30CP = \frac{650 - CP}{CP} \times 100CP \)

\(\displaystyle 30CP = \frac{100CP(650 - CP)}{CP}\)

The CP on the right hand side cancels (its on the top and bottom of the fraction

\(\displaystyle 30CP = 100(650 - CP) \)

(Divide both sides by 10)
\(\displaystyle 3CP = 10(650 - CP)\)

Expand Brackets (this gives step 3)
\(\displaystyle 3CP = 6500 - 10CP \)

Add 10CP to both sides
\(\displaystyle 3CP + 10CP= 6500 - 10CP + 10CP \)

Cancel This gives step 4
\(\displaystyle 13CP= 6500\)

This is because:
10CP + 3CP = 13CP
-10CP + 10CP =0CP =0