If we use the simple interest formula I=PrT, the principle (P) would be 6000. Assuming that it is based on annual interest, the time (t) would be 1/12. Then, you multiply 6000 by 1/12 to get 500. Finally you divide 192/500 and then multiply by 100.
If the time is based on monthly payments, then do the same thing, except multiply 6000 by 1
If you are told that a relation is a direct proportion, and you are given one data point, you can find k. The you can write the equation of the direct relation.
Here is an example. The price of gasoline follows a direct variation. John bought 5 gallons of gas and paid $15. a) Write an equation for the relation. b) Using the relation you found, how much do 13.8 gallons cost?
Solution: Since the relation is a direct variation, it follows the general equation of a direct variation:
y = kx
We are given one data point, 5 gallons cost $15. We plug in 5 for x and 15 for y and we find k.
y = kx 15 = k * 5 k = 3
Now that we know that k = 3, we rewrite the relation using our value of k.
y = 3x
This is the answer to part a).
Part b)
We use our relation, y = 3x, and we plug in 13.8 into x and find y.
The simplest fraction for is . Write the upper bound as a fraction with the same denominator:
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Hence the range for would be:
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If the denominator of is also , then the range for its numerator (call it ) would be . Apparently, no whole number could fit into this interval. The reason is that the interval is open, and the difference between the bounds is less than .
To solve this problem, consider scaling up the denominator. To make sure that the numerator of the bounds are still whole numbers, multiply both the numerator and the denominator by a whole number (for example, 2.)
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At this point, the difference between the numerators is now . That allows a number ( in this case) to fit between the bounds. However, can't be written as finite decimals.
Try multiplying the numerator and the denominator by a different number.
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It is important to note that some expressions for can be simplified. For example, because of the common factor .