Brian has money in two savings accounts. One rate is 5% and the other is 10%. If he has $900 more in the 10% account and the total interest is $273, how much is invested in each savings account?

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Question:

Brian has money in two savings accounts. One rate is 5% and the other is 10%. If he has $900 more in the 10% account and the total interest is $273, how much is invested in each savings account?

Answers:1220 dollars invested at 5% interest rate.2120 dollars invested at 10% interest rate.===============================================Explanation:Label the two accounts A and B.Account A earns 5% interestAccount B earns 10% interestBrian 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----------Start with account A over the course of t = 1 year.i = P*r*ti = x*0.05*1i = 0.05xthen compute the interest for account B (use t = 1 also).i = P*r*ti = (x+900)*0.10*1i = 0.10x + 90---------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 = 2730.15x+90-90 = 273-900.15x = 1830.15x/0.15 = 183/0.15x = 1220This means $1220 was invested at 5% interest.x+900 = 1220+900 = 2120and $2120 was invested at 10% interest.---------Check:If you invested $1220 in account A, then you earni = P*r*ti = 1220*0.05*1i = 61 dollars in interestIf you invest $2120 in account B, then you earni = P*r*ti = 2120*0.10*1i = 212 dollars in interestSo you get a total of 61+212 = 273 dollars in interest from both accounts. This confirms the two answers.

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