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mina [271]
3 years ago
7

Samantha took out two loans totaling $6000 to pay for her first year of college. She narrowed the maximum amount she could at 3.

5% simple annual interest and the remainder at 7% simple annual interest. At the end of the first year, she owed $259 in interest. How much was bolorrowed
Mathematics
1 answer:
Dovator [93]3 years ago
5 0

Our simple interest formula is I = prt, where I is the amount of interest, p is the amount of principal, r is the percentage written as a decimal, and t is the amount of time (in this case in years).  We will define our variable x as the amount borrowed at the lower percentage rate.  Our formula would then look like

.  (Remember that when we convert percentages to decimals, we divide by 100; 3.5/100 = 0.035.)

The remaining money borrowed was invested at 7% interest.  The expression to represent the remaining money would be 6000 - x, as it is what was left over to borrow.  The interest formula for this loan would be

. (Again, we must divide 7 by 100 to convert the percentage; 7/100=0.07.)

Using the distributive property we have:

(t in this case is 1, since it is 1 year.)

The total amount of interest for both loans for one year was $259, so we have:


Combine our like terms:


Cancel 420 by subtracting:


Cancel -0.035 by dividing:


This means she borrowed $4600 at the lower interest rate.  The remainder would be $6000-$4600=$1400 at the higher interest rate.




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<h3>What is a function?</h3>

The function is an expression, rule, or law that defines the relationship between one variable to another variable. Functions are ubiquitous in mathematics and are essential for formulating physical relationships.

The inverse of the logarithmic function f(x) = \log_{0.5} x is f^{-1}(x) = 0.5^x

For x = −1 in the inverse function, then the value of a will be

f^{-1}(x) = 0.5^{-1}\\\\f^{-1}(x) = 2

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For x = 0 in the inverse function, then the value of b will be

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More about the function link is given below.

brainly.com/question/5245372

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