You split $1500 between two savings accounts. Account A pays annual 5% interest and Account B pays 4% annual interest. After one year,you have earned a total of $69.50 in interest. How much money did you invest in each account?
$950
Let's assume the amount of money invested in Account A is x dollars. Since the total amount of money invested is $1500, the amount invested in Account B would be $1500 - x dollars.
The interest earned from Account A would be 5% of the amount invested, which is 0.05x dollars.
The interest earned from Account B would be 4% of the amount invested, which is 0.04($1500 - x) dollars.
According to the given information, the total interest earned from both accounts is $69.50. Therefore, we can set up the equation:
0.05x + 0.04($1500 - x) = $69.50
Simplifying the equation, we get:
0.05x + 0.04($1500) - 0.04(x) = $69.50
0.05x + $60 - 0.04x = $69.50
0.01x + $60 = $69.50
0.01x = $69.50 - $60
0.01x = $9.50
x = $9.50 / 0.01
x = $950
Therefore, $950 was invested in Account A, and $1500 - $950 = $550 was invested in Account B.
To determine how much money you invested in each account, let's assign variables to the unknowns. Let's say you invested x dollars in Account A and y dollars in Account B.
According to the problem, the amount of money you invested in both accounts adds up to $1500. So we have the equation: x + y = 1500.
Next, we need to consider the interest rates on both accounts. Account A pays a 5% annual interest rate, which can be expressed as 0.05 in decimal form. Account B pays a 4% annual interest rate, which is equivalent to 0.04 in decimal form.
Now, let's calculate the total interest earned after one year. The interest earned from Account A can be calculated using the formula 0.05x, and the interest earned from Account B can be calculated using the formula 0.04y. Since the total interest earned is $69.50, we have the equation: 0.05x + 0.04y = 69.50.
We now have a system of equations consisting of two equations:
x + y = 1500
0.05x + 0.04y = 69.50
To solve this system of equations, we can use substitution or elimination. Here, let's solve by elimination.
Multiply both sides of the second equation by 100 to eliminate decimals:
5x + 4y = 6950
Now, let's multiply both sides of the first equation by 4 to make the coefficients of y the same:
4x + 4y = 6000
By subtracting the second equation from the first equation, we can eliminate y:
(4x + 4y) - (5x + 4y) = 6000 - 6950
Simplifying the equation gives:
-1x = -950
x = 950
Now that we have the value of x, we can substitute it back into either of the original equations to solve for y. Let's use the first equation:
950 + y = 1500
y = 1500 - 950
y = 550
Therefore, you invested $950 in Account A and $550 in Account B.
amount at 5% --- x
amount at 4% --- 1500-x
.05x + .04(1500-x) = 69.50
times 100
5x + 4(1500-x) = 6950
continue, its easy