Answer: the amount invested at 8% is $16500
the amount invested at 9.5% is $20500
Explanation:
Let x represent the amount invested at 8%.
Let y represent the amount invested at 9.5%.
A women invests 37,000, part at 8% and the rest at 91/2 annual interest. It means that
x + y = 37000
The formula for simple interest is expressed as
I = PRT/100
Where
P represents the principal
R represents interest rate
T represents time in years
I = interest after t years
Considering the 8% investment,
T =1 year
P = $x
R = 8%
Therefore
I = (x × 8 × 1)/100
I = 0.08x
Considering the 9.5% investment,
T =1 year
P = $y
R = 9.5%
Therefore
I = (y × 9.5 × 1)/100
I = 0.095y
If the 91/2% investment provides 627.50 more income than the 8% investment, it means that
0.095x - 0.08x = 627.5 - - - - - - -1
Substituting x = 37000 - y into equation 1, it becomes
0.095y - 0.08(37000 - y) = 627.5
0.095y - 2960 + 0.08y = 627.5
0.095y + 0.08y = 627.5 + 2960
0.175y = 3587.5
y = 3587.5/0.175
y = 20500
x = 37000 - y = 37000 - 20500
x = 16500