Question

Todd invests $4300 in two different accounts. The first account paid 9 %, the second account paid 7 % in interest. At the end of the first year he had earned $347 in interest. How much was in each account?

Answer 1

hello

the initial principal in each account is unknown. we have a combined principal here and also a combined interest.

interest A + interest B = total interest

the rate in account A = 9%

the rate in account B = 7%

let x represent the amount of money invested in A

`\begin{gathered} 0.09* x+0.07*(4300-x)=347 \\ 0.09x+301-0.07x=347 \\ 0.02x+301=347 \\ \text{0}.02x=347-301 \\ 0.02x=46 \\ (0.02x)/(0.02)=(46)/(0.02) \\ x=2300 \end{gathered}`

the amount in the first account with an interest of 9% is $2300

now we can use this information to find the amount in the second account by simply subtracting $2300 from the sum total principal

the amount invested in both accounts which is $4300

`\begin{gathered} y=4300-2300 \\ y=2000 \end{gathered}`

the amount invested in both accounts are $2300 and $2000 respectively