help with cost price(CP) problem

**mathnoob123** · May 10th 2010, 02:59 AM

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

**SpringFan25** · May 23rd 2010, 03:52 AM

These are both standard algebra rearrangements.

Start from:
$30 = \frac{650 - CP}{CP} \times 100$

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

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

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

$30CP = 100(650 - CP)$

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

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

Add 10CP to both sides
$3CP + 10CP= 6500 - 10CP + 10CP$

Cancel This gives step 4
$13CP= 6500$

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

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