The total amount Noah has = $6300
Let the amount he invested in the first bank = x
Let the amount he invested in the second bank = y
(Amount invested in 1st bank) + (Amount invested in 2nd bank) = Total amount
x + y = 6300...........(1)
Annual Interest = $2947
Let us calculate the annual interest paid by each bank
Note: There are 12 months in ayear
Interest = (Principal x Rate x Time) / 100
Annual Interest paid by the 1st bank = (3 * x * 12) / 100
Interest paid by the 1st bank = 0.36x
Interest paid by the 2nd bank = (5 * y * 12) / 100
Interest paid by the 2nd bank = 0.05(12)y = 0.6y
(Interest paid by the 1st bank) + (Interest paid by the 2nd bank) = Annual Interest rate
0.36x + 0.6y = 2947.......(2)
Make x the subject of the formula in equation (1)
x = 6300 - y...........(3)
Substitute equation (3) into equation (2)
0.36(6300 - y) + 0.6y = 2947
2268 - 0.36y + 0.6y = 2947
2268 + 0.24y = 2947
0.24y = 2947 - 2268
0.24y = 679
y = 679 / 0.24
y = $2829.17
Put the value of y into equation (3)
x = 6300 - 2829.17
x = $3470.83