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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?

Respuesta :

Answer:

2300 AT 3.5% AND 2700 AT 5.5%

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

[tex]\begin{gathered} A_1=P_1r_1t \\ A_1=P_{2.}r_2t \end{gathered}[/tex]

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

[tex]\begin{gathered} A_1=0.055P_1 \\ A_2=0.035(400+P_1) \end{gathered}[/tex]

and since P1+P2 = 299, the above gives

[tex]A_1+A_2=0.055P_1+0.035(400+P_1)=229[/tex][tex]0.055P_1+0.035(400+P_1)=229^{\square}[/tex]

Expanding the left hand side gives

[tex]0.055P_1+0.035P_1+22=229_{}[/tex]

which simplifies to give

[tex]0.09P_1+22=229[/tex]

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

[tex]\begin{gathered} 0.09P_1=207_{} \\ P_1=2300 \end{gathered}[/tex]

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!

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