SOLUTION: Pricing: If a component of an item is 24% of (100%) the total item. This item's value is increased by 20%, what will the total % value of the whole item be increased by?

Question 764693: Pricing:
If a component of an item is 24% of (100%) the total item.
This item's value is increased by 20%, what will the total % value of the whole item be increased by?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
the item is equal to 24% of the total.
the item is increased by 20%
about the easiest way to do this is to give it some numbers.
assume the total cost is 100 dollars.
assume the item costs 24 dollars (.24 * 100 = 24)
increase the item cost by 20% to get:
24 + .2 * 24 = 24 + 4.8 = 28.8
since the item cost has increased by 4.8 dollars, then the total cost has increased by 4.8 dollars as well, so you get:
item cost = 28.8, total cost = 104.8.
percentage of item cost is now 28.8 / 104.8 * 100% = 27.48091603%
you can also do this with variable instead of numbers.
assume x is the total cost.
assume .24x is the item cost.
increase the item cost by 20% to get an item cost of .24x + .2 * .24x = .288x
the total cost has increased by the same amount, so the total cost has increased from x to x + .2 * .24x = 1.048 x.
the ratio of the new item cost to the new total cost is equal to .288x / 1.048x which is equal to .27480916034 which is equal to 27.48091603%
the calculator is doing some rounding because the number of display decimal places is less when you multiply the ratio by 100.
the whole isea is that the item has increased by a certain amount which means that the total has increased by the same amount.
putting it into numbers is about the easiest way to handle it.
any nunber will do.
calling the total 100 is easy because 24% of 100 is equal to 24.

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