You invested $27,000 in two accounts paying 2% and 3% annual interest, respectively.If the total interest earned for the year was $ 800, how much was invested at each rate?
x + y = 27000
.02x + .03 y = 800
Interest = amount times rate times time
Usually people multiply by 100 to get rid of the decimals.
x + y = 27000
2x + 3y = 80000
Multiply the first equation by -2
-2x-2y =-54000
2x + 3y = 80000
add the two equations together to solve for y which tells you how much was invested at 3%.
Subtract that from the 27000 to find out how much was invested at 2%
Let's assume that you invested x dollars at the 2% interest rate and y dollars at the 3% interest rate.
According to the given information, the total amount invested is $27,000, so we can write the equation:
x + y = 27,000 --- Equation 1
The total interest earned for the year is $800, which can be calculated using the formula:
0.02x + 0.03y = 800 --- Equation 2
To solve these equations, we can use the method of substitution or elimination. Let's use the substitution method.
From Equation 1, we can rewrite it as x = 27,000 - y.
Now, we substitute this value of x into Equation 2:
0.02(27,000 - y) + 0.03y = 800
Multiply and distribute:
540 - 0.02y + 0.03y = 800
Combine like terms:
0.01y = 800 - 540
0.01y = 260
Divide by 0.01:
y = 26,000
Now, substitute this value of y into Equation 1:
x + 26,000 = 27,000
x = 27,000 - 26,000
x = 1,000
Therefore, you invested $1,000 at a 2% interest rate and $26,000 at a 3% interest rate.
To find out how much was invested at each rate, we can set up a system of equations based on the given information.
Let's use variables to represent the amounts invested in each account. Let's call the amount invested at 2% interest rate "x" and the amount invested at 3% interest rate "y".
The total amount invested is $27,000, so we have our first equation:
x + y = 27,000
The total interest earned for the year is $800. To calculate the interest earned from each account, we can multiply the amount invested in each account by the respective interest rate and sum them up:
0.02x + 0.03y = 800
Now, we have a system of equations:
x + y = 27,000
0.02x + 0.03y = 800
We can solve this system of equations to find the values of x and y. One way to solve it is by using the method of substitution.
First, isolate one variable in the first equation. Let's solve for x:
x = 27,000 - y
Substitute this value of x into the second equation:
0.02(27,000 - y) + 0.03y = 800
Multiply and simplify:
540 - 0.02y + 0.03y = 800
0.01y = 260
y = 26,000
Now that we know y is $26,000, we can substitute it back into the first equation to find x:
x + 26,000 = 27,000
x = 27,000 - 26,000
x = 1,000
Therefore, $1,000 was invested at 2% interest and $26,000 was invested at 3% interest.