Question

Mr. Levy borrowed money from two lenders. One lender charged 5.5% simple interest and the other charged 3.5% simple interest. Mr. Levy had to borrow $400 more at 5.5% than he did at 3.5%. If the total interest after the first year was $229, how much did he borrow at each rate?

Answer 1

2300 AT 3.5% AND 2700 AT 5.5%

Step-by-step explanation:

Let us call P1 the amount borrowed at 3.5% interest rate and P2 the amount borrowed at 5.5%.

Using simple interest we have

`\begin{gathered} A_1=P_1r_1t \\ A_1=P_(2.)r_2t \end{gathered}`

since r1 = 0.055, r2 = 0.035, t =1, and P2 = P1 + 400, we have

`\begin{gathered} A_1=0.055P_1 \\ A_2=0.035(400+P_1) \end{gathered}`

and since P1+P2 = 299, the above gives

`A_1+A_2=0.055P_1+0.035(400+P_1)=229`
`0.055P_1+0.035(400+P_1)=229^(\square)`

Expanding the left hand side gives

`0.055P_1+0.035P_1+22=229_{}`

which simplifies to give

`0.09P_1+22=229`

FInally, we subtract 22 and divide both sides by 0.09 to get

`\begin{gathered} 0.09P_1=207_{} \\ P_1=2300 \end{gathered}`

Hence, the amount borrowed at 5.5% is 2300; therefore, the amount borrowed at 3.5% is

P2 = 2300+ 400

P2 = 2700

which is our answer!