Answer:
$1420 was invested in the 7% account.
$1870 was invested in the 8% account.
Explanation:
- We will need a system of equations to find the amounts invested in each account.
- We can allow x to represent the amount invested in the 7% account and y to represent the amount invested in the 8% account.
- For our system, we need to use the decimal forms of the interest rates (i.e., 0.07 and 0.08)
First equation:
We know that the sum of the interests from both accounts equals the total interest:
(7% interest rate * investment) + (8% interest rate * investment) = total interest
Since the total interest is $249, our first equation is given by:
0.07x + 0.08y = 249
Second equation:
Since Ean has 450 more in the 8% account, our second equation is given by:
y = x + 450
Method to solve: Substitution:
We can first find x (i.e., the amount invested in the 7% account) by substituting x + 450 for y in the first equation (i.e., 0.07x + 0.08y = 249):
Finding x, the amount invested in the 7% account:
0.07x + 0.08(x + 450) = 249
0.07x + 0.08x + 36 = 249
(0.15x + 36 = 249) - 36
(0.15x = 213) / 0.15
x = 1420
Thus, $1420 was invested in the 7% account.
Finding y, the amount invested in the 8% account:
Now we can find y (i.e., the amount invested in the 8% account) by plugging in 1420 for x in the second equation (i.e., y = x + 450):
y = 1420 + 450
y = 1870
Thus, $1870 was invested in the 8% account.