Alice took out a $15,000 loan for college. She is borrowing money from two banks. Bank A charges an interest rate of 6%, and Bank B charges an interest rate of 7%. After one year, Alice owes $960 in interest. How much money did she borrow from Bank A?
"0.6x + 0.7y = $960"
0.6 = 6%
0.7 = 7%
x = Bank B amount
y = Bank A amount
"x + y =$15,000 ="
Both x and y should equal $15,000 when added together.
You solve for y by solving on both sides, and you get "15,000 - x" onto the right, and "y =", on the left.
With this, you substitute in into "0.6x + 0.7y = 15,000".
This, should now look: ".06x+.07(15,000-x)=960"
Now, you solve for x, and you should be getting "x = $9,000" as your answer.
I hope this helps! :)
P.S. I got a lot of information from Y-a-h-o-o-A-n-s-w-e-r-s, but I made it into something you can understand a little better.
I meant to say "0.6x + 0.7y = 960" instead of "0.6x + 0.7y = 15,000"!
Let's assume that Alice borrowed x dollars from Bank A.
The interest charged by Bank A would be 6% of x, which is 0.06x.
Alice borrowed $15,000 in total, so she borrowed (15,000 - x) dollars from Bank B.
The interest charged by Bank B would be 7% of (15,000 - x), which is 0.07(15,000 - x).
According to the problem, the total interest Alice owes after one year is $960. So we can set up the equation:
0.06x + 0.07(15,000 - x) = 960
Simplifying the equation:
0.06x + 1050 - 0.07x = 960
Combining like terms:
-0.01x = -90
Dividing both sides by -0.01:
x = -90 / -0.01
x = 9000
Therefore, Alice borrowed $9000 from Bank A.
To find out how much money Alice borrowed from Bank A, we can set up an equation based on the given information.
Let's assume that Alice borrowed x dollars from Bank A. Since the interest rate of Bank A is 6%, the interest she owes to Bank A after one year would be 0.06x dollars.
Alice borrowed $15,000 in total, which means she borrowed $15,000 - x dollars from Bank B. The interest she owes to Bank B after one year, with an interest rate of 7%, would be 0.07($15,000 - x) dollars.
According to the given information, Alice owes a total of $960 in interest. So we can write the equation as follows:
0.06x + 0.07($15,000 - x) = $960
Now, let's solve this equation to find the value of x, which represents the amount Alice borrowed from Bank A.
0.06x + 0.07($15,000 - x) = $960
Multiply 0.07 by $15,000 and distribute:
0.06x + $1,050 - 0.07x = $960
Combine like terms:
-0.01x + $1,050 = $960
Subtract $1,050 from both sides:
-0.01x = $960 - $1,050
-0.01x = -$90
Divide both sides by -0.01 to solve for x:
x = -$90 ÷ -0.01
x = $9,000
Therefore, Alice borrowed $9,000 from Bank A.