I invested $3,000, part at 2% and the rest at 5% simple interest. After 1 year, I earned a total of $117 in interest. How much did I invest at each rate?
just add up the interest. With $x at 2%,
.02x + .05(3000-x) = 117
x = 1100
To solve this problem, we can use a system of equations. Let's start by assigning variables to the unknown amounts. Let x represent the amount invested at 2% and y represent the amount invested at 5%.
According to the problem, the total amount invested is $3,000, so we have the equation:
x + y = 3000 --(Equation 1)
Now let's consider the interest earned. The interest on the amount invested at 2% can be calculated using the formula:
Interest = Principal * Rate * Time
For the amount invested at 2%, the interest earned is:
0.02x
Similarly, the interest on the amount invested at 5% is:
0.05y
According to the problem, the total interest earned after 1 year is $117. So we have the second equation:
0.02x + 0.05y = 117 --(Equation 2)
Now we need to solve this system of equations to find the values of x and y. There are several methods to solve systems of equations, such as substitution or elimination. In this case, we will use the elimination method.
To eliminate one variable, we will multiply both sides of Equation 1 by -0.02:
-0.02(x + y) = -0.02 * 3000
-0.02x - 0.02y = -60 --(Equation 3)
Now let's add Equation 2 and Equation 3 together:
0.02x + 0.05y - 0.02x - 0.02y = 117 - 60
Simplifying, we get:
0.03y = 57
To solve for y, we divide both sides of the equation by 0.03:
y = 57 / 0.03
y = 1900
Now we can substitute the value of y into Equation 1 to find x:
x + 1900 = 3000
x = 3000 - 1900
x = 1100
Therefore, you invested $1,100 at 2% and $1,900 at 5%.