Final answer:
To solve the problem, two equations are established to represent the total amount and total interest earnings for the sums held in two different interest-bearing accounts. By solving the set of equations, it was determined that $600 was invested at 3% interest and $800 at 4% interest.
Step-by-step explanation:
Calculating Investments with Different Interest Rates
Assuming the interest is simple interest and the interest period is the same for both accounts, we can set up two equations to determine the amount of money in each account. Let x be the amount at 3% interest, and y be the amount at 4% interest. We know two things:
The total amount of money is $1400: x + y = 1400
The total interest from both accounts is $50: 0.03x + 0.04y = 50
To solve these linear equations, we can use substitution or elimination. Using substitution, we express y in terms of x from the first equation: y = 1400 - x. We plug this into the second equation:
0.03x + 0.04(1400 - x) = 50
Solving for x gives us the amount at 3% interest:
0.03x + 56 - 0.04x = 50
-0.01x = -6
x = 600
Therefore, $600 is invested at 3% and $800 (1400 - 600) at 4%.