Katie invested a total of $7,000, part at 2% simple interest, and part at 3% simple interest. At the end of 1 year, the investments earned, $184.00 interest. How much was invested at each rate?
Well, it seems like Katie was "investing" in her own comedy routine! She put some money at 2% simple interest and the rest at 3% simple interest. At the end of the year, she earned a total of $184.00 in interest. Now, let's do some math that's worthy of applause!
Let's say Katie invested x dollars at 2% interest. This means that her investment would earn 0.02x dollars in interest.
Next, she invested the remaining amount (7000 - x) at 3% interest, which would earn her 0.03(7000 - x) dollars in interest.
According to the information given, the total interest earned was $184.00. So, we can set up an equation: 0.02x + 0.03(7000 - x) = 184.
Now, we can put on our makeup, juggle some numbers, and solve for x:
0.02x + 0.03(7000 - x) = 184
0.02x + 210 - 0.03x = 184
-0.01x = -26
x = 2600
Haha, Katie invested $2,600 at 2% interest! That means the other chunk of her money, (7000 - 2600) = $4,400, was invested at 3% interest. Ta-da!
Let's assume Katie invested x dollars at 2% interest and (7000 - x) dollars at 3% interest.
The interest earned on x dollars at 2% interest is given by (x * 0.02).
The interest earned on (7000 - x) dollars at 3% interest is given by ((7000 - x) * 0.03).
According to the given information, the total interest earned is $184.
So, we can form the equation: (x * 0.02) + ((7000 - x) * 0.03) = 184.
Simplifying the equation, we get: 0.02x + 210 - 0.03x = 184.
Combining like terms, we have: -0.01x = -26.
Dividing both sides by -0.01, we find: x = 2600.
Therefore, Katie invested $2600 at 2% interest and (7000 - 2600) = $4400 at 3% interest.
To solve this problem, we can use a system of equations. Let's call the amount invested at 2% interest rate as 'x' and the amount invested at 3% interest rate as 'y'.
Since we know the total amount invested is $7,000, we can write the first equation as:
x + y = 7000
Now let's focus on the interest earned. The interest from the investment at 2% interest rate can be calculated as 0.02 * x (2% expressed as a decimal). The interest from the investment at 3% interest rate can be calculated as 0.03 * y (3% expressed as a decimal). Since the total interest earned is $184.00, we can write the second equation as:
0.02 * x + 0.03 * y = 184
Now we have a system of equations:
x + y = 7000
0.02 * x + 0.03 * y = 184
We can solve this system of equations to find the values of x and y.
One approach is substitution. Solve the first equation for x:
x = 7000 - y
Now substitute this value of x into the second equation:
0.02 * (7000 - y) + 0.03 * y = 184
140 - 0.02 * y + 0.03 * y = 184
0.01 * y = 184 - 140
0.01 * y = 44
y = 44 / 0.01
y = 4400
Therefore, Katie invested $4,400.00 at 3% simple interest rate.
Now substitute this value of y back into the first equation to solve for x:
x + 4400 = 7000
x = 7000 - 4400
x = 2600
Therefore, Katie invested $2,600.00 at 2% simple interest rate.
invested at 2% --- x
invested at 3% --- 7000-x
.02x + .03(7000-x) = 184
carry on