select a set of equations.mary invested one amount a %10 simple invest, and a second amount at %3 interest, earning $21.72 in one year. If she would have earned $15.07. What were the two amounts?
To solve this problem, let's set up a system of equations. Let's denote the first amount Mary invested as 'x' and the second amount as 'y.'
According to the problem, Mary invested one amount at 10% simple interest and another amount at 3% interest, earning $21.72 in one year. This can be written as:
0.10x + 0.03y = 21.72 ... Equation (1)
The problem also states that if Mary had earned $15.07, the equation can be written as:
0.10x + 0.03y = 15.07 ... Equation (2)
Now, we have a system of equations:
0.10x + 0.03y = 21.72 ... Equation (1)
0.10x + 0.03y = 15.07 ... Equation (2)
To solve this system of equations, we can use the method of elimination or substitution. Let's use elimination:
Subtract equation (2) from equation (1):
(0.10x + 0.03y) - (0.10x + 0.03y) = (21.72 - 15.07)
Simplifying, we get:
0 = 6.65
This seems to be an inconsistency since 0 cannot be equal to 6.65. Thus, the system of equations is inconsistent, and there is no solution that satisfies both equations.
Therefore, we cannot determine the two amounts Mary invested based on the given information.