SOLUTION: a businessman invested different amounts at 8%,8.75% and 9%, all simple annual interest. altogether he has invested php400,000 and earns php34,550 per year.how much has he invested

Question 244918: a businessman invested different amounts at 8%,8.75% and 9%, all simple annual interest. altogether he has invested php400,000 and earns php34,550 per year.how much has he invested at each rate if he has invested php40,000 more at 9% than 8%?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
a businessman invested different amounts at 8%,8.75% and 9%, all simple annual interest. altogether he has invested php400,000 and earns php34,550 per year.how much has he invested at each rate if he has invested php40,000 more at 9% than 8%?
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Equations:
Quantity Eq.::::x + y + z = 400,000
Interest Eq.::0.08x + 0.0875y + 0.09z = 34550
Relative Eq: z = y + 40,000
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Modify and Rearrange:
x + y + z = 400,000
800x + 875y + 900z = 345500000
0x + y - z = -40,000
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I used the TI matrix function and got:
x = 114285.71 (amt. invested at 8%
y = 122857,14 (amt. invested at 8.75%
z = 162857.14 (amt. invested at 9%
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Cheers,
Stan H.
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