Question

That's your Danny had $20,000 to invest. He invest some of it in an account that paid 7% simple interest per year, and he invested the rest in an account that paid 10% simple interest per year. After one year, he received a total of $1580 in interest.how much did he invest in each account.first account $second account $

Answer 1

Let the principal of the investment be represnted below

$p_1=20000-p_2$

Therefore,

$\begin{gathered} I=\frac{prt}{100} \\ for\text{ the first one } \\ I=\frac{(20000-p_2)\times7\times1}{100}=\frac{140000-7p_2}{100} \\ \end{gathered}$$\begin{gathered} \text{For the second one} \\ I=\frac{p_2\times10\times1}{100}=\frac{10p_2}{100}=\frac{p_2}{10} \end{gathered}$

Therefore,

$\begin{gathered} \frac{140000-7p_2}{100}+\frac{p_2}{10}=1580 \\ \frac{140000-7p_2+10p_2}{100}=1580 \\ 140000-7p_2+10p_2=158000 \\ 3p_2=158000-140000 \\ p_2=\frac{18000}{3} \\ p_2=6000 \end{gathered}$$\begin{gathered} P_1=20000-6000 \\ p_1=14000 \end{gathered}$

He invested $14000 in the first account and $6000 in the second account.