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Question 12351: I am having trouble figuring out how to use the identity property of 1 (how it works) on various problems. For instance here are two:
Leon left a 15 percent tip for a meal, the total cost of the meal, including tip, was $41.40. What was the cost of the meal before tip?
(In this problem we divide 41.40 by 1.15, how do we know we have to add 1 to the .15)
Here's where I'm confused, between these two problems.
credit cards: The balance in Will's Mastercard account grew 2 percent, to $870 in one month. What was his balance at the beginning of the month?
(somehow we use I think .98 to this problem) how do we know we have to subtract .02 from 1)
Please help me, in figuring why we subtract or add 1. How do we know which operation to use and how it works.
Answer by rapaljer(4671)   (Show Source):
You can put this solution on YOUR website! The 1 comes from 100%. In your first problem, you said that the TOTAL bill, including the tip was $41.40. This means that you have the cost of the meal, which is 100% of the meal PLUS 15% of the meal for the TIP. That would be 115%.
Another way of looking at this is to say
Let x = cost of the meal.
.15x = amount of the tip (since it is 15% of the meal cost)
The equation is based upon the fact that the total is
x + .15x = 41.40
Do you see that the x in this equation represents 1x? That's where the 1 comes from!!
In the case of a DISCOUNT, you would be subtracting the discount from 100% instead of adding it. This is apparently how you came up with the 98% in your second illustration. However, take another look at that. I think your second illustration should ALSO be an add-on, since it began with x at the beginning of the month, and then it grew 2% to end up with $870. I think that should be the same situtation as when you added the tip to end up with a total amount.
R^2 at SCC
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