Scott invested a total of $9500 at two separate banks. One bank pays simple interest of 11% per year while the other pays simple interest at a rate of 9% per year. If Scott earned $973.00 in interest during a single year, how much did he deposit in each bank?
x = 11%
y = 9%
x + y = 9500
11x + 9y = 97300
x = 5900
y = 3600
Oh, Scott and his banking adventures! Let's solve this money puzzle with a dash of humor.
Let's call the amount Scott deposited at the bank with 11% interest "x" dollars. That means the amount he deposited at the bank with 9% interest is "9500 - x" dollars.
Now, to calculate the interest earned at each bank:
The interest earned at the bank with 11% interest is 0.11x dollars.
The interest earned at the bank with 9% interest is 0.09(9500 - x) dollars.
And since Scott earned a total of $973.00, we can set up an equation:
0.11x + 0.09(9500 - x) = 973
Now let's put our fancy math hat on and solve it:
0.11x + 0.09(9500 - x) = 973
0.11x + 855 - 0.09x = 973
0.02x + 855 = 973
0.02x = 118
x = 5900
So, Scott deposited $5900 at the bank with 11% interest and $3600 at the bank with 9% interest.
Keep those banking adventures going, Scott, and maybe consider investing in a clown costume! It'll make banking a lot more fun! *honk honk*
Let's assume that the amount Scott invested in the bank paying 11% interest is X dollars.
Therefore, the amount Scott invested in the bank paying 9% interest is (9500 - X) dollars.
Now, let's calculate the interest earned at each bank.
The interest earned at the bank paying 11% interest is (11/100) * X dollars.
The interest earned at the bank paying 9% interest is (9/100) * (9500 - X) dollars.
According to the given information, the total interest earned in a year is $973.00.
Therefore, we can form the equation:
(11/100) * X + (9/100) * (9500 - X) = $973.00
Simplifying the equation:
11X/100 + 9(9500 - X)/100 = 973.00
Multiplying through by 100 to remove the fractions:
11X + 9(9500 - X) = 97300
Expanding and simplifying:
11X + 85500 - 9X = 97300
2X + 85500 = 97300
2X = 97300 - 85500
2X = 11800
X = 11800/2
X = 5900
Therefore, Scott invested $5900 in the bank paying 11% interest.
To calculate the amount invested in the other bank, we can subtract this amount from the total amount invested:
9500 - 5900 = $3600
So, Scott invested $5900 in the bank paying 11% interest and $3600 in the bank paying 9% interest.
To solve this problem, we can set up a system of equations. Let's denote the amount Scott invested at the bank with 11% interest as "x" and the amount he invested at the bank with 9% interest as "y".
Since we know that the total amount Scott invested is $9500, the first equation is:
x + y = 9500 (equation 1)
Now let's determine the interest earned at each bank. The interest earned at the bank with 11% interest can be found by multiplying the amount invested by the interest rate (in decimal form) and the time period:
0.11x (equation 2)
Similarly, the interest earned at the bank with 9% interest is:
0.09y (equation 3)
According to the information given, the total interest earned during the year is $973. So, our third equation is:
0.11x + 0.09y = 973 (equation 4)
Now, we have a system of equations:
x + y = 9500 (equation 1)
0.11x + 0.09y = 973 (equation 4)
We can solve this system of equations to find the values of x and y.
One way to solve it is by elimination. Multiply equation 1 by 0.11 to make the coefficient of x match with the coefficient of x in equation 4:
0.11(x + y) = 0.11(9500)
0.11x + 0.11y = 1045 (equation 5)
Now, subtract equation 5 from equation 4 to eliminate x:
(0.11x + 0.09y) - (0.11x + 0.11y) = 973 - 1045
0.11x - 0.11x + 0.09y - 0.11y = -72
-0.02y = -72
y = -72 / -0.02
y = 3600
Substitute the value of y into equation 1 to solve for x:
x + 3600 = 9500
x = 9500 - 3600
x = 5900
Therefore, Scott deposited $5900 at the bank with 11% interest and $3600 at the bank with 9% interest.