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Sagot :
Formula for simple interest:
A = P(1 + rt)
P = Principal
r = interest rate (r1 = 5% and r2 = 10%)
t = time in years (1 year)
In the first account:
A = P(1 + rt)
A1 = P1(1 + 0.05)
In the second account:
A2 = P2(1 + 0.10)
Also A1 + A2 = 1075
And P1 + P2 = 1000
If we use both account equations in the third equation:
A1 + A2 = 1075
P1(1 + 0.05) + P2(1 + 0.10) = 1075
1.05 P1 + 1.10 P2 = 1075
P1 = (1075 -1.10 P2)/1.05
Since P1 + P2 = 1000
then (1075 -1.10 P2)/1.05 + P2 = 1000
(1075 -1.10 P2) + 1.05 P2 = 1000 (1.05) = 1050
1075 - 1.10 P2 + 1.05 P2 = 1050
-0.05 P2 = 1050 - 1075 = -25
P2 = -25/(-0.05) = 500
P1 = 1000 - P2 = 1000 - 500 = 500
Answer:
In the 5% account Helene invested: 500
In the 10% account Helene invested: 500
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