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=(prt)/(100) \\ for\text{ the first one } \\ I=((20000-p_2)*7*1)/(100)=(140000-7p_2)/(100) \\ \end{gathered}`
`\begin{gathered} \text{For the second one} \\ I=(p_2*10*1)/(100)=(10p_2)/(100)=(p_2)/(10) \end{gathered}`

Therefore,

`\begin{gathered} (140000-7p_2)/(100)+(p_2)/(10)=1580 \\ (140000-7p_2+10p_2)/(100)=1580 \\ 140000-7p_2+10p_2=158000 \\ 3p_2=158000-140000 \\ p_2=(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.