Respuesta :
Answer: $6000 was invested at 4.5% and $4000 was invested at 5%.
Step-by-step explanation:
Let x represent the amount that you invested at 4.5% simple interest.
Let y represent the amount that you invested at 5% simple interest.
You invested a total of 10,000 at 4/2% and 5% simple interest. . This means that
x + y = 10000
The formula for determining simple interest is expressed as
I = PRT/100
Considering the amount invested at 4.5% interest,
P = $x
T = 1 year
R = 4.5℅
I = (x × 4.5 × 1)/100 = 0.045x
Considering the amount invested at 5% interest,
P = $y
T = 1 year
R = 5℅
I = (y × 5 × 1)/100 = 0.05y
During one year, the two accounts earned $470. it means that
0.045x + 0.05y = 470 - - - - - - - - - -1
Substituting x = 10000 - y into equation 1, it becomes
0.045(10000 - y) + 0.05y = 470
450 - 0.045y + 0.05y = 470
- 0.045y + 0.05y = 470 - 450
0.005y = 20
y = 20/0.005
y = 4000
x = 10000 - y = 10000 - 4000
x = 6000
