Answer:
$18000 was invested at 12%
$3500 was invested at 15%
Explanations:
Let the amount invested in the first account be P₁
Let the amount invested in the scond account be P₂
A total of $21500 was invested in the two accounts
That is:
P₁ + P₂ = 21500................(1)
Interest = Principal x Rate x Time
Time = 1 year
Rate charged on the first account, R₁ = 12% = 12/100 = 0.12
Rate charged on the second account, R₂ = 15% = 15/100 = 0.15
Interest on first account = P₁ x R₁ x T
Interest on first account = P₁ x 0.12 x 1 = 0.12P₁
Interest on second account = P₂ x R₂ x T
Interest on second account = P₂ x 0.15 x 1 = 0.15P₂
The total interest charged is $2685
(Interest on first account) + (Interest on second account) = Total interest
0.12P₁ + 0.15P₂ = 2685.................................(2)
Make P₁ the subject of the formula from equation (1)
P₁ = 21500 - P₂...............................(3)
Sustitute equation (3) into equation (2)
0.12 ( 21500 - P₂) + 0.15P₂ = 2685
2580 - 0.12P₂ + 0.15P₂ = 2685
0.03P₂ = 2685 - 2580
0.03P₂ = 105
P₂ = 105/0.03
P₂ = 3500
Substitute the value of P₂ into equation (3)
P₁ = 21500 - 3500
P₁ = 18000
$18000 was invested at 12%
$3500 was invested at 15%