Answers:
1220 dollars invested at 5% interest rate.
2120 dollars invested at 10% interest rate.
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Explanation:
Label the two accounts A and B.
Account A earns 5% interest
Account B earns 10% interest
Brian invests x dollars in account A and x+900 dollars in account B.
Using the formula, i = P*r*t, we can compute the simple interest for both accounts
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Start with account A over the course of t = 1 year.
i = P*r*t
i = x*0.05*1
i = 0.05x
then compute the interest for account B (use t = 1 also).
i = P*r*t
i = (x+900)*0.10*1
i = 0.10x + 90
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Over the course of 1 year, Brian earns 0.05x dollars in interest with account A and also 0.10x+90 dollars in interest with account B.
In total he earns 0.05x+0.10x+90 = 0.15x+90 dollars in interest.
We're told this amount of interest he earns is $273, so,
0.15x+90 = 273
0.15x+90-90 = 273-90
0.15x = 183
0.15x/0.15 = 183/0.15
x = 1220
This means $1220 was invested at 5% interest.
x+900 = 1220+900 = 2120
and $2120 was invested at 10% interest.
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Check:
If you invested $1220 in account A, then you earn
i = P*r*t
i = 1220*0.05*1
i = 61 dollars in interest
If you invest $2120 in account B, then you earn
i = P*r*t
i = 2120*0.10*1
i = 212 dollars in interest
So you get a total of 61+212 = 273 dollars in interest from both accounts. This confirms the two answers.
