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30 votes
30 votes
Susan invests 2 times as much money at 6 % as she does at 5 %. If her total interest after 1 year is $510, howmuch does she have invested at each rate?Susan invests $___at 5% and $___ at 6%.

User Carson Myers
by
2.5k points

1 Answer

15 votes
15 votes

The interest formula is :


I=Prt

where I = interest

P = Principal amount

r = interest rate

t = time in years

From the problem, Susan invested twice the amount at 6% as she does at 5%.

If she invested P to 5%, the amount she invested to 6% will be 2P

Using the formula to calculate the two interests.

For 5% :


\begin{gathered} I=P(0.05)(1) \\ I=0.05P \end{gathered}

For 6% :


\begin{gathered} I=2P(0.06)(1) \\ I=0.12P \end{gathered}

The sum of the interests is $510

This will be :


\begin{gathered} 0.05P+0.12P=510 \\ \text{Solve for P :} \\ 0.17P=510 \\ P=(510)/(0.17)=3000 \end{gathered}

She invested $3000 for 5% and $6000 for 6%

The answers are :

5% : $3000

6% : $6000

User Henklein
by
2.8k points
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