Problem #5
Business and finance. Kevin earned $165 interest for 1 year on an investment of $1500. At the same rate, what amount of interest would be earned by an investment of $2500?
My answer is: The amount of interest would be $275 earned by an investment of $2500.
Problem #6
Simplify each complex fraction.
((w+3)/(4w)) / ((w-3)/(2w))
My answer is: (w+3)/(2w-6)
Yes for #1. #2 could also be written
(w+3)/([2(w-3)]
It depends upon what you consider "simplified".
For problem #5, to determine the amount of interest earned by an investment of $2500, you can use the concept of proportionality.
Step 1: Calculate the interest rate
The interest rate for the investment can be found by dividing the interest earned ($165) by the principal amount ($1500):
Interest rate = Interest earned / Principal = $165 / $1500 = 0.11
Step 2: Apply the interest rate to the new principal
Now, use the interest rate of 0.11 to calculate the interest earned for the new principal amount of $2500:
Interest earned = Interest rate * Principal = 0.11 * $2500 = $275
Therefore, the correct answer is $275 earned by an investment of $2500.
For problem #6, to simplify the complex fraction, you need to combine the fractions in the numerator and denominator and cancel out any common factors.
Step 1: Combine the fractions in the numerator and denominator
((w+3)/(4w)) / ((w-3)/(2w)) can be written as:
((w+3) * (2w)) / ((4w) * (w-3))
Step 2: Cancel out the common factors
In the numerator, (w+3) cancels out with 2w, and in the denominator, 4w cancels out with (w-3):
((w+3) * (2w)) / ((4w) * (w-3)) = (w+3)/(2(w-3))
Therefore, the simplified form of the complex fraction is (w+3)/(2(w-3)).
Please note that there can be alternative forms that are also considered simplified depending on the context of the problem.