Answer: $4900 at 8%
$6000 at 11%
Step-by-step explanation:
Let x represent the amount which he invested in the account paying 8% interest.
Let y represent the amount which he invested in the account paying 11% interest.
Jose invests $10900 in two different accounts. The first account paid 8 %, the second account paid 11 % in interest. This means that
x + y = 10900
The formula for determining simple interest is expressed as
I = PRT/100
Considering the account paying 8% interest,
P = $x
T = 1 year
R = 8℅
I = (x × 12 × 1)/100 = 0.08x
Considering the account paying 11% interest,
P = $y
T = 1 year
R = 11℅
I = (y × 6 × 1)/100 = 0.11y
At the end of the first year he had earned $1052 in interest., it means that
0.08x + 0.11y = 1052 - - - - - - - - - -1
Substituting x = 10900 - y into equation 1, it becomes
0.08(10900 - y) + 0.11y = 1052
872 - 0.08y + 0.11y = 1052
- 0.08y + 0.11y = 1052 - 872
0.03y = 180
y = 180/0.03
y = 6000
x = 10900 - y = 10900 - 6000
x = 4900
or